Calculate the area of a right trapezoid with the longer base ($b_1$) being 9 cm, the shorter base ($b_2$) being one-third of the longer base, and the height ($h$) being 7 cm.

1. Problem Description

Calculate the area of a right trapezoid with the longer base ($b_1$) being 9 cm, the shorter base ($b_2$) being one-third of the longer base, and the height ($h$) being 7 cm.

2. Solution Steps

First, determine the length of the shorter base, $b_2$, which is one-third of the longer base, $b_1$.

$b_1 = 9$ cm

$b_2 = \frac{1}{3} \times b_1 = \frac{1}{3} \times 9 = 3$ cm

Next, recall the formula for the area $A$ of a trapezoid:

$A = \frac{1}{2} (b_1 + b_2) \times h$

Substitute the values of $b_1$, $b_2$, and $h$ into the formula:

$A = \frac{1}{2} (9 + 3) \times 7 = \frac{1}{2} (12) \times 7 = 6 \times 7 = 42$

3. Final Answer

The area of the right trapezoid is 42 cm$^2$.