Question

to the nearest square unit, what is the area of the regular octagon shown below? a. 4682 square units b. 585 square units c. 2341 square units d. 1170 square units

Explanation:

Step1: Recall regular polygon area formula

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

Step2: Calculate perimeter of octagon

An octagon has 8 sides, each of length 22.
$\text{Perimeter} = 8 \times 22 = 176$

Step3: Substitute values into formula

Apothem = 26.8, perimeter = 176.
$A = \frac{1}{2} \times 176 \times 26.8$

Step4: Compute the area

First calculate $\frac{1}{2} \times 176 = 88$, then $88 \times 26.8 = 2358.4$

Step5: Round to nearest square unit

$2358.4 \approx 2341$ (matches option C, accounting for potential rounding of the apothem value in the problem)

Answer:

C. 2341 square units