+1310 A pentagon is drawn by placing an isosceles right triangle on top of a square as pictured. What percent of the area of the pentagon is the area of the right triangle?
+128475 Area of square = s^2
Area of isoceles right triangle = (1/2)(s/√2)^2 = (1/2) [(s^2) / 2] = (1/4)s^2
So...the area of the pentagon = s^2 + (1/4) s^2 = (5/4)s^2
So....the triangle is [ (1/4)s^2 ] / [ (5/4)s^2 ] = (1/4) / (5/4) = (1/4) (4/5) = 4/20 = 1/5 of the pentagon's area = 20%
+128475 Area of square = s^2
Area of isoceles right triangle = (1/2)(s/√2)^2 = (1/2) [(s^2) / 2] = (1/4)s^2
So...the area of the pentagon = s^2 + (1/4) s^2 = (5/4)s^2
So....the triangle is [ (1/4)s^2 ] / [ (5/4)s^2 ] = (1/4) / (5/4) = (1/4) (4/5) = 4/20 = 1/5 of the pentagon's area = 20%
