Question

Find the area of an isosceles right triangle with hypotenuse 40 cm.

Answer 1

Given: Isosceles right triangle with hypotenuse = 40 cm.

Stepwise calculation:

1. Let the equal legs of the isosceles right triangle each be x cm.

2. By Pythagoras theorem, 

Hypotenuse² = leg² + leg²

⇒ 40² = x² + x²

⇒ 1600 = 2x²

⇒ x² = 800

3. The area of the triangle 

= `1/2` × base × height 

= `1/2 xx x xx x`

= `1/2 xx x^2`

= `1/2 xx 800`

= 400 cm²

The area of the isosceles right triangle with hypotenuse 40 cm is 400 cm².