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

Find the area of the regular polygon. Round your answer to the nearest hundredth.-example-1
User Thibaultbl
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1 Answer

18 votes
18 votes

Answer:

Explanation:

The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.

Use the tan of the angle so formed (which is 30 degrees)

Tan(30)= opposite / height (which is the line you just drew).

Tan(30) = 3.5 / h

Tan(30) = 0.5774

Tan(30) = 3.5 / h multiply both sides by h

h*Tan(30) = 3.5 Divide by tan30

h = 3.5 / Tan(30)

h = 3.5 / 0.5774

h = 6.062

Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.

Area of 1 triangle = 1/2 * b * h

area of 1 triangle = 1/2 * 7 * 6.062

Area of 1 triangle = 21.2176

There are 6 such triangles so multiply that number by 6

Answer: 6 * 21.2176

Answer: 127.31

User Michael Walter
by
3.3k points
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