Question

Write a ratio in simplified form of the area of the shaded figure to the area of the figure that encloses it.

Answer 1

Trapezoid area equals: height * base =
6w * (10 + 6w) = 36w² + 60w

Square area equals: side² = (6w)² = 36w²

The ratio equals:
36w² / (36w² + 60w) = 36w² / 6w(6w + 10)

The simplified form:
6w / (6w + 10)

Good luck

Answer 2

First, let's start by finding the Areas for both shaded and not shaded.

-Area of the shaded area = Length²
Area of the shaded area = 6² = 36
-Area of the not shaded region = $\frac{LH}{2}$ 
Area of the not shaded region = $\frac{5*6}{2}$
                                                    = $\frac{30}{2}$
                                                    = 15
Now, Let's make our ration!
Area of shaded : Area of not shaded
           36            :               15
           12             :                5