Question

what is the area of the irregular pentagon?
(image of an irregular pentagon with side lengths 14 in, 12 in, 8 in, 9 in)

Explanation:

Step1: Split shape into rectangle + triangle

First, calculate the base of the triangle: $14 - 8 = 6$ in.
Calculate the height of the triangle: $12 - 9 = 3$ in.

Step2: Find area of rectangle

Area formula: $\text{length} \times \text{width}$
$\text{Area}_{\text{rectangle}} = 12 \times 8 = 96$ in²

Step3: Find area of triangle

Area formula: $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 6 \times 3 = 9$ in²

Step4: Sum the two areas

Total area = rectangle area + triangle area

Answer:

$96 + 9 = 105$ square inches