Question

Prove that the area of any quardrilateral with perpendicular diagonals = 1/2 ×product of diagonal​

Answer 1

Answer:

Area of quadrilateral = 1/2* Product of its diagonals.

Step-by-step explanation:

The quadrilateral with perpendicular diagonals may be a square or a rhombus.

Here, ABCD is a quadrilateral with perpendicular diagonals intersecting at I.

Area of a triangle =

$\frac{1}{2} \times base \times height$

ar (∆ABD) = 1/2*BD*AI .... (1)

ar (∆CBD) = 1/2*BD*CI .... (2)

By adding equation (1)& (2),

ar (∆ABD) + ar (∆CBD) = 1/2*BD*AI + 1/2*BD*CI

ar (ABCD) = 1/2*BD (AI+CI)

ar (ABCD)=1/2*BD*AC