The semi-perimeter of a right isosceles triangle is 4 2 + 2 cm. What is the area of the triangle?

Dear Student,


Semi-perimeter=a+b+c2     In Isosceles two sides are equal  Let  base = a   and  equal  sides =bSo, a2=b2+b2         By Pythagorasa=2b2a=b2now,we have42+2=a+2b2.........iputting value of a=b2 in equationi42+2=b2+2b282+2=2b+b282+2=b2+2b=82+22+2So, b=8a=b2a=82Now area of right isosceles triangle is =12×b×b                                                                    =12×8×8=32 cm2
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wait im doing it
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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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