Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals - Maths - Areas of Parallelograms and Triangles

Question

Prove that the area of a rhombus is equal to half the
rectangle contained by its diagonals

Aakash Sharma · Accepted Answer

Let the diagonal of the rhombus be d1 and d2 where d1 > d2 $Thus area of rhombus = \frac{1}{2} \times d_{1} \times d_{2} (1)$ Now the rectangle contained by of diagonals of rhombus will have length (l) and breadth (b) as d1 and d2 So area of rectangle = l Ã— b = d1 Ã— d2 (2) From (1) and (2) $A rea of rhombus = \frac{1}{2} area of rectangle$

Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.