Question

the trapezoids at right are similar.
hint 1:
refer to the math notes box in lesson 3.1.2.
hint 2:
use proportional equations to find the missing dimensions.
refer to the math notes box in lesson 3.1.3.
more help:
the formula to find the area of a trapezoid is \\( \frac { 1 } { 2 } h ( b _ { 1 } + b _ { 2 } ) \\)
a. what is the ratio of the heights?
b. compare the areas. what is the ratio of the areas?

Explanation:

Step1: Find the ratio of heights

The heights of the trapezoids are \(11\) cm and \(33\) cm.
The ratio of the heights is \(\frac{11}{33}=\frac{1}{3}\)

Step2: Find the ratio of areas

For similar figures, if the ratio of corresponding linear dimensions (like height) is \(k\), the ratio of their areas is \(k^{2}\).
Since the ratio of heights \(k = \frac{1}{3}\), the ratio of areas is \((\frac{1}{3})^{2}=\frac{1}{9}\)

Answer:

a. The ratio of the heights is \(\frac{1}{3}\)
b. The ratio of the areas is \(\frac{1}{9}\)