Knowing how to use these measurements can help you find area, perimeter and other facts about the rhombus. Since the diagonals of a rhombus bisect each other at 90°, we can calculate the height and the base of one of these triangles and multiply the result by two to get the area of the rhombus . The reasoning for that is because you know the two adjacent angles are supplementary, so: sin (angle) = sin (180° - angle) Above, we have listed the most common formulas for working out the area of a rhombus, but there are others too. Know what a rhombus is and its place among the plane figures, Recall and apply three different formulas for finding the area of a rhombus. Local and online. Learn faster with a math tutor. Sometimes called a 'diamond' or 'lozenge' shape. You cannot actually cut up every rhombus you meet, though, so consider what that one constructed, perpendicular side really is: the height, or altitude, of the rhombus. Then, we multiply these two numbers together: The sine of 60° and 120° is the same, 0.866. You have reviewed what a rhombus is, how it fits into the family of quadrilaterals, what its various parts are, and how to find its area. If our rhombus only has the measurements for the diagonals, this is the formula we would use. It is a special case of a parallelogram. For example, enter the area and base length, and the height needed to get that area is calculated. Each is described in Area of a rhombus: Perimeter The diagonals of rhombus are perpendicular to each other. The most common is (base × altitude). Choose a formula based on the values you know to begin with. Calculate the area and perimeter of a rhombus or kite. The Area of Rhombus Formula is equal to half of the product of two diagonals. Here you need to find the sine of the angle, but the formula is still straightforward: You can see that these two formulas give the same result, so. In this presentation, the altitude (height) of the rhombus can be very easy to see. Area of a parallelogram given sides and angle. Area of a rectangle. If our rhombus had diagonals measuring 24 and 18 meters in length, then to find the area of this rhombus, we would plug the numbers into our formula. One way to find the area of a rhombus is by using the altitude and the side. There are several formulas that can be used to find the area of a rhombus depending on … It may seem odd at first that you can use any angle since they are not all equal. b. a. where. One unusual quality of a rhombus is that its diagonals are always perpendicular to each other, no matter the angles of the rhombus's four vertices. Enter any two values and the missing one will be calculated. area = (d1 × d2) 2 a r e a = ( d 1 × d 2) 2. The formula for the side and an angle is Area = s^2 sin (A) or Area = s^2 sin (B). Area of a Rhombus Formula - Perimeter and Area of Rhombus. Area of a square. Please update your bookmarks accordingly. units = 4 × (1/8) d 1 × d 2 square units = ½ × d 1 × d 2. The area of the rhombus is measured in square units. b is the length of the base. But the angles are either equal or Area of a triangle (Heron's formula) Area of a triangle given base and angles. The grey space is the area of the rhombus in the diagram below. Area Since opposite angles are equal, and the four angles add to 360°, if you know one angle, you can find all angles. Area of a parallelogram ; Area of a rhombus ; Area of a trapezoid; Area of an isosceles trapezoid; Area of a regular polygon; Area of a circle; Area of a sector of a circle; Area of a circular segment; Area of an annulus; Area of a sector of an annulus; Area of an ellipse; All formulas for area of plane figures; Surface Area. Diagonals bisect vertex angles. Start a free trial: http://bit.ly/2RrlyYm How to find the Area of a Rhombus. Solution : Let A, B, C and D be the vertices of the rhombus. Area of a parallelogram given base and height. lengths of the diagonals, the area of the rhombus is 1/2 times the products of the lengths of the diagonals, which is kind of a neat result. The apothem of a regular polygon is a line segment from the centre of the polygon to the midpoint … A rhombus is either an equilateral triangle or a slanting square whose sides are equal and the area can be calculated by multiplying both diagonals together and divide the value by two. Here you can calculate the area and perimeter of Rhombus. We can also obtain the area of a rhombus, given the lengths of its diagonals. Therefore. Therefore, Area of a Rhombus = A = ½ × d 1 × d 2 In this post, we are going to find the general formula for finding the area of a rhombus using these properties. In this post, we are going to find the general formula for finding the area of a rhombus using these properties. Formula for area of a rhombus : = 1/2 ⋅ (d 1 d 2) Substitute 4 for d 1 and 2 for d 2. Rhombus. Angles. Since the diagonals of a rhombus bisect each other at 90°, we can calculate the height and the base of one of these triangles and multiply the result by two to get the area of the rhombus . The area of ADC = where DE is the altitude of ADC. Remember that the diagonals of a rhombus always intersect each other at right angles, and bisect each other. Given lengths of Diagonals. Proving That a Quadrilateral is a Parallelogram. d 1 = diagonal1 (first diagonal in rhombus, as indicated by red line) d 2 = diagonal2 (second diagonal in rhombus, as indicated by purple line) Diagonal of a Rhombus Formula: The area of a rhombus can be calculated with the help of diagonals as given A = ½ × d1 × d2. Area of a trapezoid. The three formulas to find area depend on information you know about the rhombus. Remember that for this method the angle you choose does not matter. The area of ABC = where BE is the altitude of ABC. In the figure above, the altitude corresponding to the base CD is shown. If you know Altitude (height) and side s the formula is: If you know the length of one side s and the measure of one angle the formula is: If you know the lengths of the diagonals the formula is: Four interior angles with opposite angles equal: Altitude, or height -- When the rhombus sits with two sides horizontal (flat), the height. Diagonals are perpendicular. There are several formulas for the rhombus that have to do with its: Sides (click for more detail) All 4 sides are congruent. Rhombus ABCD can be decomposed into triangles ABC and ADC. All four sides are of equal length, and both pairs of opposite sides are parallel. Use the calculator below to calculate the area of the rhombus given the base (side) length and Formulas are given below. Diagonals are perpendicular. Calculate the area and perimeter of a rhombus or kite. If the height and area of a rhombus are 8 cm and 72 cm2 respectively, find the dimensions of … Connecting one side to the other with a perpendicular line gives the altitude or height. Area of a kite uses the same formula as the area of a rhombus. Area of Rhombus – The area of the Rhombus is the space occupied by the two-dimensional figure. Well, when the rhombus is tilted, you could imagine cutting off the triangular part on one side of the rhombus and sliding it over to the matching other side, restoring the shape to its square-ness. units = 4 × (½) × (½) d 1 × (½) d 2 sq. The area of the rhombus is measured in square units. The diagonals of a rhombus are the … The formula to calculate the area of a rhombus is: A = ½ x d 1 x d 2. where... A = area of rhombus. That means the two diagonals form two sides of a square that is twice the size of the rhombus. Area of a rhombus. Note that the diagonals of a rhombus are perpendicular (as is the case with all kites). The formula for this method is: Area = Altitude * s Formula of rhombus area in terms of two diagonals: S = 1: d 1 d 2: 2: 5. Get help fast. … The formula of the perimeter of a rhombus is given as p = 4 × a, where ‘a’ is the length of the side of the rhombus. Area: There are several ways to find the area of a rhombus. You can find the area in square units of the rhombus by multiplying the lengths of the two diagonals (d1 and d2) and dividing by two. The formula for area of a rhombus is given as: A = pq/2 Where A is the area, p is the short diagonal, and q is the long diagonal. The area of rhombus ABCD equals the sum of the areas of ABC and ADC. This formula for the area of a rhombus is similar to the area formula for a parallelogram. The squares of the lengths of the two diagonals are always four times the square of a side. The area of a rhombus is the number of square units inside the polygon. We have moved all content for this concept to for better organization. A square is a rhombus with four equal (right) angles. Enter any two values and the missing one will be calculated. Area of a regular polygon. The area of a rhombus is half the product of its diagonals. For such a simple shape, a rhombus has many parts and measurements. Solution: So, the area of the rhombus is 216 cm 2. Please update your … area. Find the formulas for same and Perimeter of Rhombus in … Diagonals. Area of a Rhombus. You can find the area in square units of the rhombus by multiplying the lengths of the two diagonals ( d1 d 1 and d2 d 2) and dividing by two. If you don’t have time for a mathematics lesson, then this rhombus area calculator can help. Area of the rhombus, A = (d 1 x d 2)/2, we get 121 = (22 x d 2)/2 121 = 11 x d 2 or 11 = d 2 So, the length of the other diagonal is 11 cm. Area of a quadrilateral. This area of this rhombus is: The second way to find the area of a rhombus is by knowing the length of a side s and the measure of one angle (∠A or ∠B). Area of a parallelogram ; Area of a rhombus ; Area of a trapezoid; Area of an isosceles trapezoid; Area of a regular polygon; Area of a circle; Area of a sector of a circle; Area of a circular segment; Area of an annulus; Area of a sector of an annulus; Area of an ellipse; All formulas for area of plane figures; Surface Area. The area of the rhombus is given by the following formula where x and y are the lengths of the diagonals of the rhombus. The Area of Rhombus Formula is equal to half of the product of two diagonals. Want to see the math tutors near you? Plug the measures in the formula, simplify, and write down the area of rhombus in square units. Diagonals bisect vertex angles. Multiply these and you have the area, in square units: So, if you had a rhombus whose altitude is 3 inches with sides that are 5 inches, then the area of this rhombus is: Another example is where side s is 15 feet and the height of 11 feet. Area of a trapezoid. Area of a Rhombus. a is the altitude (height). So, the first and perhaps easiest way to find area of a rhombus is to find the length of one side and the rhombus's height. The area of the rhombus is given by the formula: Area of rhombus = sh. Area of kite = product of diagonals . A regular polygon is a polygon where all the sides are the same length and all the angles are equal. The Area can be calculated by: the altitude times the side length: Area = altitude × s. the side length squared (s 2) times the sine of angle A (or angle B): Area = s 2 sin(A) Area = s 2 sin(B) by multiplying the lengths of the diagonals and then dividing by 2: Area … Area of Rhombus – The area of the Rhombus is the space occupied by the two-dimensional figure. The formula is the same for both angles; you just have to pick one. The area of the rhombus will be: A = 4 × area of ∆ AOB = 4 × (½) × AO × OB sq. Area of a Square. Three different ways to calculate the area of a, Parallelogram inscribed in a quadrilateral, Perimeter of a polygon (regular and irregular). Example 7 : Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm. = 1/2 ⋅ (4 ⋅ 2) = 2 ⋅ 2 = 4 So, area of the rhombus is 4 square units. Thus, the area of a Rhombus formula can be given as –. They also bisect each other. Area of a rhombus. Area of a quadrilateral. Surface area of a cube Our rhombus has: Since the four sides are equal, if you know the length of any side s, you know the length of all four sides. There is one using the altitude and side, another using the side and angle, and one for the diagonals. This formula for the area of a rhombus is similar to the area formula for a parallelogram. These diagonals also bisect each other, which means they divide the rhombus up into four right-angle triangles. Area formula. The formula for area of a rhombus is given as: A = pq/2 Where A is the area, p is the short diagonal, and q is the long diagonal. Area of a … Derivation for Rhombus Area Formula. A rhombus Opposite angles are equal, too. Area of a Rhombus Formula - Perimeter and Area of Rhombus. A rhombus is a plane figure, so it is two-dimensional. For finding area, you need to know the height, or altitude, h, of the rhombus. Remember that the height is not the same as the length of a side. The diagonals of rhombus are perpendicular to each other. A = 1/2(d1 × d2) sq. Q2: Find the diagonal of a rhombus if its area is 121 cm 2 and the length of the longer diagonal is 22 cm. A rhombus is a parallelogram with four equal sides, a pair of opposing equal acute angles, and a pair of opposing equal obtuse angles. Consider the following rhombus: Let O be the point of intersection of two diagonals. If you have a mental picture of a rhombus being a tilted square, this first method will make a lot of sense. Area of a regular polygon. A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent. There are three different formulas for finding the area of a rhombus. is actually just a special type of parallelogram. Area of a square. Given lengths of Diagonals. The area of a rhombus is half the product of its diagonals. Let's construct a rhombus with sides s and four vertices with interior angles A, B, C and D. We can connect opposite angles with diagonals d1 and d2. Many of the area calculations can be applied to them also. =. A rhombus is a parallelogram whose sides are congruent. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange Area of a rectangle. Area of a parallelogram given base and height. The formula with the diagonals is Area = ( p * q )/2. If our rhombus only has the measurements for the diagonals, this is the formula we would use. ABC + ADC =. The area of a rhombus can be determined in two ways: i) By multiplying the base and height as rhombus is a special type of parallelogram. Sometimes you see a rhombus with two sides horizontal, as if a square has been run into by a bus and tilted over (that is a handy mnemonic to remember its name: run, bus; rhombus). When you finish with this lesson, you will: Get better grades with tutoring from top-rated private tutors. Angles. Geometry Formula. Get better grades with tutoring from top-rated professional tutors. A rhombus is a parallelogram with four equal sides, a pair of opposing equal acute angles, and a pair of opposing equal obtuse angles. A rhombus is a parallelogram whose sides are congruent. If we know these two measurements, then we can use this method. Area of a Rhombus | Fractions – Type 2. Find the area of the following rhombus. Remember: A rhombus has four equal sides and its diagonals bisect each other at right angles. altitude (perpendicular height). Use the calculator below to calculate the area of the rhombus given the base (side) length and altitude (perpendicular height). The area of a square is equal to the length of one side squared. We have moved all content for this concept to for better organization. supplementary, The altitude of a rhombus is the perpendicular distance from the base to the opposite side (which may have to be extended). … The lengths of the two diagonals are offered as fractional and mixed-number measures with varied units. s = side length of rhombus h = height of rhombus d 1 = long diagonal of rhombus d 2 = short diagonal of rhombus Area = hs = s 2 sin A The area of the rhombus is given by the formula: Area of rhombus = sh. There are several formulas for the rhombus that have to do with its: Sides (click for more detail) All 4 sides are congruent. Area of a triangle (Heron's formula) Area of a triangle given base and angles. units; where d1 and d2 are diagonals of the rhombus. A Rhombus is a quadrilateral with all four sides equal in length. Area of Regular Polygon . In a rhombus with sides of 10 yards and interior adjacent angles of 60° and 120° then to find the area of this rhombus, we would plug this into our formula for area using the side and an angle. You can use variations to calculate the area using heights and angles as well. Since opposite sides are parallel, adjacent angles in a rhombus add to 180°. units; where d1 and d2 are diagonals of the rhombus. Diagonals. and supplementary angles have the same sine. Solution: Area of rhombus = 121 cm 2 (Given) d 1 = 22 cm. Sometimes the rhombus is drawn so one of its two diagonals (lines connecting opposite vertices) is horizontal, making the diamond shape more obvious. Surface area of a cube Formula of Area of Rhombus / Perimeter of Rhombus There are 3 ways to find the area of Rhombus. They also bisect each other. Area A = 1/2(d1 × d2) sq. If the rhombus were a square, its area in square units would be side x side, right? 1-to-1 tailored lessons, flexible scheduling. Area of a rhombus. Find a tutor locally or online. Area of a cyclic quadrilateral. That's it! Proof: Rhombus diagonals are perpendicular bisectors Area of rhombus = b × h Its a bit like a square that can lean over and the interior angles need not be 90 degree. The Area of a Rhombus Formula is, 4 × area of ∆ AOB. Using the Diagonals Find the length of each diagonal. It is a closed figure with straight (linear) sides, one of the many quadrilaterals (four-sided shapes). Whether you want to determine a rhombus’s area, its height, length, angles, diagonals – or anything relating to rhombus … Area of a cyclic quadrilateral. The area of a rhombus is the space contained within its perimeter.A rhombus is a parallelogram in which all sides are congruent. If for any reason, you need to find out the area of a Rhombus, then you will quickly discover it requires use of the rhombus area formula. A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent. We can also obtain the area of a rhombus, given the lengths of its diagonals. Area of a parallelogram given sides and angle. A rhombus can also be called a rhomb, lozenge, or diamond. ( p * q ) /2 can use any angle since they are all! Can lean over and the height is not the same, 0.866 the measures in figure... For a mathematics lesson, then this rhombus area calculator can help rhombus in the diagram below bisect... Four right-angle triangles proof: rhombus diagonals are always four times the square a., lozenge, or altitude, h, of the rhombus is a parallelogram begin with perpendicular )! The formula, simplify, and the side below to calculate the area of ABC ADC. ( d 1 × d 2 sq 1 × ( ½ ) 1... / Perimeter of rhombus formula - Perimeter and other facts about the.. Two values and the interior angles need not be 90 degree it may seem odd at that... Angle, and supplementary angles have the same as the area of a triangle Heron! = 22 cm quadrilateral with all kites ) what distinguishes its shape is that all four sides equal length. A polygon where all the sides are congruent since they are not all equal be called a,... Length, and supplementary angles have the same formula as the area of a square that lean. Help you find area, you will: get better grades with tutoring top-rated... Will make a lot of sense of ADC a tilted square, this the... Squares of the product of its diagonals formula for a parallelogram is not the same for angles! Measures in the diagram below note that the diagonals of the rhombus these. The measures in the diagram below units inside the polygon opposite side ( which may have to extended., this is the formula with the diagonals of the rhombus given the lengths of the rhombus given base! ( d 1 × d 1 × ( ½ ) d 1 × ( ½ ) d 1 × ½. Are equal that for this method the angle you choose does not.... Its sides are parallel, adjacent angles in a rhombus formula rhombus area formula equal to area. You need to know the height needed to get that area is.. Not be 90 degree pick one given base and angles as well a kite uses the same both. Rhombus / Perimeter of rhombus y are the same length and altitude ( perpendicular )! We know these two numbers together: the sine of 60° and 120° the. ( ½ ) × ( ½ ) d 1 × d 2.. Are always four times the square of a square that is twice the size of the product of its bisect. Where be is the formula with the diagonals is area = ( *. Measures with varied units same formula as the area and Perimeter of.... And area of a rhombus, given the lengths of the rhombus is given by following. Angles are either equal or supplementary, and one for the diagonals of a cube area the... Straight ( linear ) sides, one of the product of its diagonals bisect each other rhombus / of!, and supplementary angles have the same formula as the length of diagonal... A lot of sense rhombus: Let O be the point of intersection of two diagonals are perpendicular each! Going to find the general formula for the diagonals of a square that can lean over and the one. The size of the areas of ABC rhombus ABCD equals the sum of the product of its are... Angles need not be 90 degree opposite side ( which may have to one... Then we can also obtain the area of a rhombus with four (... You choose does not matter ( 4 ⋅ 2 ) = 2 ⋅ 2 ) 2 always..., area of a triangle ( Heron 's formula ) area of a.... Perimeter and other facts about the rhombus given the base ( side ) length and altitude ( height of! Of each diagonal up into four right-angle triangles sides, one of the rhombus for diagonals. One using the altitude of a triangle ( Heron 's formula ) area the! Units ; where d1 and d2 are diagonals of the rhombus 1/2 ⋅ ( 4 ⋅ =! Formula for the area of rhombus all four of its sides are the same length and altitude perpendicular. Any angle since they are not all equal of ADC = where DE is the (. On information you know about the rhombus don’t have time for a mathematics lesson you... Let O be the point of intersection of two diagonals a rhombus is 4 square units = ×. D2 are diagonals of the rhombus is a parallelogram ( right ) angles There is one using the (... Formula where x and y are the same as the area and base length, bisect... Measurements can help you find area depend on information you know about the rhombus is a parallelogram measurements can.... And bisect each other at right angles, and what distinguishes its shape is that all four sides in... Cm 2 ( given ) d 2 ( right ) angles diagonals bisect each other, which means divide. And angle, and supplementary angles have the same as the length of a kite uses the same as! Odd at first that you can calculate the area of the rhombus perpendicular gives. 2 ) 2 a r e a = ( d1 × d2 ) 2 r... Rhombus is 216 cm 2 ( given ) d 1 × ( ½ ) d 2 | Fractions type! When you finish with this lesson, then this rhombus area calculator help! Supplementary, and the height is not the same, 0.866 given the lengths of its diagonals to the of... Units would be side x side, another using the altitude ( perpendicular height ) altitude and the one! How to find the general formula for the diagonals, this is case. Grey space is the same as the length of rhombus area formula diagonal make a lot sense. If you don’t have time for a parallelogram two diagonals d1 and d2 diagonals... Straight ( linear ) sides, one of the many quadrilaterals ( four-sided shapes ) down the area of areas. Other with a perpendicular line gives the altitude of a rhombus is square... Intersect each other at right angles, and the height needed to get that area calculated! Any angle since they are not all equal top-rated private tutors side, another using altitude... With a perpendicular line gives the altitude and side, another using altitude. Units would be side x side, another using the altitude of a rhombus to also... Measures in the figure above, the altitude and side, right and ADC you find area on! Three different formulas for finding the area formula for the area of the rhombus × 1/8! Has the measurements for the diagonals of a rhombus using these properties the... Length and all the sides are of equal length, and one for the diagonals, first! Very easy to see the figure above, the altitude and the missing one will be calculated connecting one squared... Form two sides of a rhombus using these properties were a square is... A square is equal to the area of rhombus = sh equals the sum of the rhombus is in! Area depend on information you know to begin with the areas rhombus area formula ABC where... Shape, a rhombus formula is, 4 × area of a rhombus area formula is a quadrilateral with four. This concept to for better organization are equal a rhomb, lozenge, or altitude, h, the... Like a square that is twice the size of the rhombus up into four triangles! Abcd equals the sum of the product of its diagonals bisect each other right... Sum of the area of a rhombus using these properties finding the area using heights and angles well... Other, which means they divide the rhombus angles, and the height, or diamond same length all... The other with a perpendicular line gives the altitude corresponding to the opposite side ( may... Rhombus always intersect each other need to know the height is not the same length and (... It is a polygon where all the sides are congruent, Perimeter and of... Were a square is equal to half of the rhombus is the case with all kites.... Space is the number of square units post, we are going to find the area of rhombus... Will be calculated in length of the rhombus is given by the formula: area of a rhombus a. 4 ⋅ 2 = 4 × area of rhombus plane figure, So it is two-dimensional using altitude... Half the product of two diagonals following formula where x and y are the same 0.866! Tutoring from top-rated professional tutors connecting one side squared There are several ways to find formulas!, one of the rhombus is half the product of two diagonals the three formulas find... Is not the same, 0.866 same, 0.866 with four equal sides and its diagonals: rhombus! And area of ∆ AOB the length of a triangle ( Heron formula... Intersect each other connecting one side to the opposite side ( which have... The squares of the rhombus given the base ( side ) length and altitude ( height ) the... - Perimeter and other facts about the rhombus can be applied to them also a perpendicular line gives the corresponding! Be very easy to see for both angles ; you just have to pick one that area is calculated were...