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PolarNik [594]
2 years ago
15

A regular decegom has a perimeter of 150 in and an apothem of ≈ 23.1 in. What is the area of this polygon to the nearest tenth o

f a square foot?
Mathematics
1 answer:
borishaifa [10]2 years ago
5 0

<u>Given</u>:

Given that the perimeter of a regular decagon is 150 inches.

The apothem of a regular decagon is 23.1 inches.

We need to determine the area of the polygon.

<u>Area of the regular decagon:</u>

The area of the regular decagon can be determined using the formula,

A=\frac{1}{2}ap

where a is the apothem and p is the perimeter of the polygon.

Substituting the values, we get;

A=\frac{1}{2}(23.1 \times 150)

Multiplying, we get;

A=\frac{1}{2}(3465)

Dividing, we get;

A=1732.5 \ in^2

Thus, the area of the regular decagon is 1732.5 square inches.

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Answer:

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Step-by-step explanation:

XYZ is a sector of a circle. The radius YZ is 6 inches .The angle of the sector is given as 45°. The area of the sector can be solved as follows.

area of a sector = ∅/360 × πr²

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area of a sector = 45/360 × 3.14 × 6²

area of a sector = 45/360 × 3.14 × 36

area of a sector = 45/360 × 113.04

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Answer:

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