Question

to the nearest square unit, what is the area of the regular heptagon shown below? a. 2772 square units b. 1572 square units c. 5545 square units d. 792 square units

Explanation:

Step1: Recall area formula for regular polygon

The area $A$ of a regular polygon is given by:
$$A = \frac{1}{2} \times \text{perimeter} \times \text{apothem}$$

Step2: Calculate perimeter of heptagon

A heptagon has 7 sides. Each side length is 20.8, so:
$$\text{Perimeter} = 7 \times 20.8 = 145.6$$

Step3: Substitute values into area formula

Apothem = 21.6. Plug into the formula:
$$A = \frac{1}{2} \times 145.6 \times 21.6$$

Step4: Compute the area

First calculate $\frac{1}{2} \times 145.6 = 72.8$, then:
$$A = 72.8 \times 21.6 = 1572.48$$

Step5: Round to nearest square unit

$1572.48 \approx 1572$

Answer:

B. 1572 square units