Question

What is the area of a right angled isosceles triangle whose hypotenuse is $6\sqrt{2}cm?$

• A. $12c{m}^2$
• B. $18c{m}^2$
• C. $24c{m}^2$
• D. $36c{m}^2$

Answer 1

Answer: (B)

$18c{m}^2$

In an isosceles right angled triangle, the two sides on the right angle are equal
Let the equal side be $a$
Hence, hypotenuse of the isosceles right angled triangle of side $a=\sqrt{a^2+a^2}=\sqrt{2}a$
Given, hypotenuse of the triangle $=6\sqrt{2}cm$
$\sqrt{2}a=6\sqrt{2}cm$
$a=6cm$
In the isosceles right triangle, the base and height $=a$
Hence, area of the triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times 6\times 6=18$ sq cm