Given: The perimeter of an isosceles right triangle is 4(2+√2)cm Formula Used: Area of right-angled isosceles triangle =a2∕2 Where a= equal sides of the isosceles triangle Calculation:
Given, AB=BC=x (let) In △ABC,∠B=90∘ AC2=AB2+BC2 ⇒AC2=x2+x2 ⇒AC2=2x2 ⇒AC=√2x So, Perimeter of ABC=AB+BC+CA ⇒x+x+√2x=4(2+√2) ⇒2x+√2x=4(2+√2) ⇒x(2+√2)=4(2+√2) ⇒x=4 Area of triangle =x2∕2 ⇒ Area of triangle =42∕2=8 ∴ The area of triangle is 8 square cm .