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?
+9481 Let's call the length of each leg of the right triangle " t " .
And let's call the side length of the square " s " .
The triangle is an isosceles right triangle, so
t2 + t2 = s2
2t2 = s2
And...
area of triangle = (1/2)(t * t) = t2/2
area of pentagon = area of square + area of triangle
area of pentagon = s2 + t2/2 Substitute 2t2 in for s2 .
area of pentagon = 2t2 + t2/2
So...
\(\frac{\text{area of triangle}}{\text{area of pentagon}}=\frac{\frac{t^2}{2}}{2t^2+\frac{t^2}{2}}=\frac{\frac12}{2+\frac12}=\frac12\cdot\frac25=\frac15=\frac{20}{100}\)
The area of the triangle is 20% of the area of the pentagon. 
+9481 Let's call the length of each leg of the right triangle " t " .
And let's call the side length of the square " s " .
The triangle is an isosceles right triangle, so
t2 + t2 = s2
2t2 = s2
And...
area of triangle = (1/2)(t * t) = t2/2
area of pentagon = area of square + area of triangle
area of pentagon = s2 + t2/2 Substitute 2t2 in for s2 .
area of pentagon = 2t2 + t2/2
So...
\(\frac{\text{area of triangle}}{\text{area of pentagon}}=\frac{\frac{t^2}{2}}{2t^2+\frac{t^2}{2}}=\frac{\frac12}{2+\frac12}=\frac12\cdot\frac25=\frac15=\frac{20}{100}\)
The area of the triangle is 20% of the area of the pentagon.
