# The semi-perimeter of a right isosceles triangle is $4\left(2+\sqrt{2}\right)$ cm. What is the area of the triangle?

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Isosceles triangle, dimensions are a, a and b # b is the base and a are the equal sides
semi perimeter = (a +a +b)/2 # half of the sum of the sides

It is a right isosceles triangle
thus b2 =(a2 +a2)  # base^2 = side1^2 + side2^2 where side1 and side2 are a( since they are equal
b2 = 2a2
b = 21/2a

semi perimeter is 1/2(a + a + b) = 1/2(a  +a + 21/2a )= 1/2(2a + 21/2a)  = (a/2)(2 + 21/2)

This is given to be 4(2 + 21/2)
so a/2 = 4 cm and a = 8cm
Area of right isosceles triangle is a2   = 64 sq cm

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