Question

Find the area of the regular polygon. Round your answer to the nearest hundredth

Answer 1

Answer:

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the missing side that is 1/2 the side of the missing heptagon. You have to assume that the figure is a regular heptagon, something you should point out to your teacher. Math really requires well qualified diagrams.

c^2 = a^2 + b^2

c = 2.77

a = 2.5

b = 1/2 the side of the heptagon.

2.77^2 = 2.5^2 + b^2

7.6729 =6.25 + b^2

7.5629 - 6.25 = b^2

b^2 = 1.4229

b = sqrt(1.4229)

b = 1.1928

But the side is twice that long

s = 2.3857

Now draw another line from the side you just found. It will be the same length as 2.77. It's a radius of the circumcircle.

Area of the triangle so formed is

Area = 1/2 * b * h

b = 2.3857

h = 2.5

Area = 1/2 * 2.5 * 2.3857

Area = 2.982

There are 7 such triangles.

Answer: 7 * 2.982

Answer: 20.87