Question

Find the area of the regular decagon with a side measure of 4 cm.

Give the answer to the nearest tenth. 

Question 28 options:

129.4 cm2

246.2 cm2

123.1 cm2

139.8 cm2
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Answer 1

28. One way to do this is to split it up into 10 congruent isosceles triangles whose vertices meet at the center of the decagon.

The vertex angle will be 36 degrees and base will be 4 cm.

Work out the height of one of these triangles:-

tan 18 = 2 / h

h = 2 / tan 18 = 6.155 cm

So the area of this triangle = 1/2 * 4 * 6.155 = 12.311 cm^2

So area of the decagon = 10 * 12.311 = 123.1 cm^2 to nearest tenth.

Its the 3rd choice.

Answer 2

C.
`123.1\text{ cm}^2`

Explanation:

We have been given that each side of a regular hexagon measures 4 cm. We are asked to find the area of our given hexagon.

We will use surface area of hexagon formula to solve our given problem.

`A=(5)/(2)*a^2\sqrt{5+2√(5)}`

`A=(5)/(2)*4^2\sqrt{5+2√(5)}`

`A=(5)/(2)*16\sqrt{5+2√(5)}`

`A=5*8\sqrt{5+2√(5)}`

`A=40*3.0776835371752536`

`A=123.107341487\approx 123.1`

Therefore, the area of our given hexagon is 123.1 squared cm and option C is the correct choice.