Question

In the given figure, EF is parallel to BC. If area of triangle ABC is 576 cm², the area of triangle AEF is ______.

Options

• 128 cm²

• 288cm²

• 256 cm²

• 768 cm²

Answer 1

In the given figure, EF is parallel to BC. If area of triangle ABC is 576 cm², the area of triangle AEF is 256 cm².

Explanation:

From figure,

In △ AEF and △ ABC,

⇒ ∠EAF = ∠BAC (Common angle)

⇒ ∠AEF = ∠ABC (Corresponding angle)

∴ △ AEF ~ △ ABC (By A.A. axiom)

We know that,

The areas of two similar triangles are proportional to the squares of their corresponding sides.

∴ `("Area of" △ AEF​)/("Area of" △ ABC) = (EF^2)/(BC^2)​`

⇒ `("Area of" △ AEF​)/576 ​= 8^2/12^2` 

⇒ `("Area of" △ AEF​)/576 ​= 64/144` 

⇒ Area of △ AEF = `64/144 ​× 576`

⇒ Area of △ AEF = 64 × 4

= 256 cm²