Question

What is the ratio of the areas (large to small quadrilaterals) of these two figures?

Answer 1

36 : 1

Explanation:

Consider the ratio of the side lengths of the quadrilaterals:

`(42)/(7)=(36)/(6)=6`

This means that the two given quadrilaterals are similar.

For any two similar figures, the ratio of their areas is the squares of the ratio of their side lengths.

Therefore:

`\frac{\text{ Area of Larger Figure}}{\text{ Area of Smaller Figure}}=((42)/(7))^2=(42^2)/(7^2)=(36)/(1)`

The ratio of the areas (large to small quadrilaterals) is 36:1.