A figure shows 2 similar squares, A and B, which overlap each other.

Question

The ratio of the shaded area to the total area of Square B is 3:5. The ratio of the shaded area to the total area of the Square A is 9:17. What is the ratio of the shaded area to the total unshaded areas of the figure?

Answer 1

Without a picture, it is somewhat unclear.

 

I assume that the shaded is the area of the intersection of the two squares.

 

B:

Shaded : unshaded = 3 : 5

 

A:

Shaded : Unshaded = 9 : 17.

 

For squares A and B the ratio numbers for shaded area have different numbers. These two numbers represent the same area. This means that 3 (unit B) is the same as 9 (unit A).

 

What we could do, is to write the ratio for square B so that the shaded area has the same numerical value as for square A.

B:

Shaded : Unshaded = 3:5 = 9:15.

 

Now, the shaded areas for both A and B squares have the same value.

 

Then,

Shaded : Total unshaded = 9 : (17 +15)

 

The ratio of shaded and total unshaded area is 9:32.