Question

To the nearest square unit, what is the area of the regular heptagon shown below?

A. 3566 square units
B. 1783 square units
C. 509 square units
D. 1019 square units

Answer 1

Solution 1 (informal):
hmm... this heptagon looks awfully similar to a circle! Let's use the area of a circle with 23 as the radius: pi*23*23 = 1661, the closest option is B. 1783 square units
Solution 2 (formal):
Area of a regular polygon = .5*apothem*perimeter
= .5*23*(7*22.15) = B. 1783 square units

Answer 2

The answer is B. 1783 square units

The heptagon consists of 7 triangles. So, the area of the heptagon (A) is the area of 7 triangles (7 * A1):
A = 7 * A1

The area of the triangle (A1) with sides s and height h is:
A1 = s * h / 2
A = 7 * A1 = 7 * s * h / 2

We know:
s = 22.15 unit
h = 23 unit

A = 7 * s * h / 2
A = 7 * 22.15 * 23 / 2
A = 1783.075
A ≈ 1783 square units