Question

what is the total area of the figure below? 16 in. 9 in. 8 in, 6 in. 10 in.

Explanation:

Step1: Identify the two shapes (trapezoid and triangle)

The figure consists of a trapezoid (left) and a triangle (right). For the trapezoid, the two parallel sides (bases) are 16 in and 10 in, height is 9 in. For the triangle, base is 6 in, height is 8 in.

Step2: Calculate area of trapezoid

The formula for the area of a trapezoid is $A_{trapezoid} = \frac{(b_1 + b_2)}{2} \times h$. Substituting $b_1 = 16$, $b_2 = 10$, $h = 9$:
$A_{trapezoid} = \frac{(16 + 10)}{2} \times 9 = \frac{26}{2} \times 9 = 13 \times 9 = 117$ square inches.

Step3: Calculate area of triangle

The formula for the area of a triangle is $A_{triangle} = \frac{1}{2} \times base \times height$. Substituting base = 6, height = 8:
$A_{triangle} = \frac{1}{2} \times 6 \times 8 = 3 \times 8 = 24$ square inches.

Step4: Sum the areas

Total area = $A_{trapezoid} + A_{triangle} = 117 + 24 = 141$ square inches.

Answer:

141 square inches