Rhombus is a quadrilateral in which all the sides are equal. Rhombus has all the properties of a parallelogram and its diagonals bisect each other at right angles. The area of a rhombus can be calculated using the conventional formula used to calculate the area of a parallelogram b*h where "b" is the base and "h" is the perpendicular distance between the base and the opposite parallel line.
ABCD is a rhombus and we shall derive the formula for finding out the area given its diagonals AC and BD
learning how to find area of a rhombus
Let the length AC be d1 and that of BD be d2. The formula for calculating the area of a triangle is 1/2 bh where 'b" is the base and "h" is height or altitude.
We shall consider the rhombus as the combinations of two triangles ABC and ADC.If we add the areas of triangles ABC and ADC we are sure to get the area of the rhombus ABCD.
The diagonals of rhombus bisect each other at right angles the height of triangles of ABC and ADC will be half of the diagonal BD which is equal to d2/2. We shall now calculate the area separately and add.
Formula to learn area of a rhombus
Area of triangle ABC =1/2 (d1* d2/ 2) =(d1 d2) /4
Area of triangle ADC=1/2 (d1* d2/ 2) =(d1 d2) /4
Area ABC +Area ADC = (d1 d2 )/4 + (d1 d2 ) /4 =d1 d2 /2
The area of the rhombus = 1/2 product of its diagonals
I like to share this algebra 2 formulas list with you all through my article.
learn examples on area of a rhombus
We shall illustrate this by two examples. We are given the diagonals of a rhombus as 10 cms and 12 cms. We are asked to find the area of the rhombus. The area of a rhombus= 1/2 the product of its diagonals= 1/2 *10*12 = 60 square cm.
This is an example to find the area of the rhombus using the conventional formula. Suppose the length of the side of a rhombus is given as 12cm and the perpendicular distance between the sides is given as 10 cm the area of the rhombus =side* perpendicular distance = 10 * 12 =120square cm.
ABCD is a rhombus and we shall derive the formula for finding out the area given its diagonals AC and BD
learning how to find area of a rhombus
Let the length AC be d1 and that of BD be d2. The formula for calculating the area of a triangle is 1/2 bh where 'b" is the base and "h" is height or altitude.
We shall consider the rhombus as the combinations of two triangles ABC and ADC.If we add the areas of triangles ABC and ADC we are sure to get the area of the rhombus ABCD.
The diagonals of rhombus bisect each other at right angles the height of triangles of ABC and ADC will be half of the diagonal BD which is equal to d2/2. We shall now calculate the area separately and add.
Formula to learn area of a rhombus
Area of triangle ABC =1/2 (d1* d2/ 2) =(d1 d2) /4
Area of triangle ADC=1/2 (d1* d2/ 2) =(d1 d2) /4
Area ABC +Area ADC = (d1 d2 )/4 + (d1 d2 ) /4 =d1 d2 /2
The area of the rhombus = 1/2 product of its diagonals
I like to share this algebra 2 formulas list with you all through my article.
learn examples on area of a rhombus
We shall illustrate this by two examples. We are given the diagonals of a rhombus as 10 cms and 12 cms. We are asked to find the area of the rhombus. The area of a rhombus= 1/2 the product of its diagonals= 1/2 *10*12 = 60 square cm.
This is an example to find the area of the rhombus using the conventional formula. Suppose the length of the side of a rhombus is given as 12cm and the perpendicular distance between the sides is given as 10 cm the area of the rhombus =side* perpendicular distance = 10 * 12 =120square cm.
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