If the perimeter

Given, Perimeter of isosceles right angled triangle = (√ 2+1)cm

Let the equal sides of the isosceles triangle = a cm

Then the hypotenuse = a√ 2 cm

According to the given condition

a+ a + √ 2 a = (√ 2+1)

⇒ 2a+ √ 2 a = (√ 2+1)

⇒ a (2+√ 2) = (√ 2+1)

⇒

By rationalizing the denominator

Here, In denominator a = 2 and b = √2

= cm

Now hypotenuse = a√ 2

⇒ Hypotenuse

⇒ Hypotenuse = 1cm

Area = 1/2 base × height

Here hypotenuse is the height of the right isosceles triangle

Area =

= cm²