Question

question 8 of 10
to the nearest square unit, what is the area of the regular heptagon shown
below?
image of a regular heptagon with an apothem of 21.6 and a side length of 20.8
a. 5545 square units
b. 2772 square units
c. 1572 square units
d. 792 square units

Explanation:

Step1: Recall the formula for the area of a regular polygon

The area \( A \) of a regular polygon is given by \( A=\frac{1}{2}\times perimeter\times apothem \). A regular heptagon has 7 sides.

Step2: Calculate the perimeter of the heptagon

Each side length is 20.8, so the perimeter \( P = 7\times20.8=145.6 \).

Step3: Identify the apothem

The apothem (the distance from the center to the midpoint of a side, perpendicular to the side) is given as 21.6.

Step4: Calculate the area

Using the formula \( A=\frac{1}{2}\times P\times a \), where \( P = 145.6 \) and \( a = 21.6 \).

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Rounding to the nearest square unit, we get 1572.

Answer:

C. 1572 square units