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Rus_ich [418]
3 years ago
13

A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches.

The perpendicular distance from a side to the center is 5 inches to the nearest inch. What is the perimeter of the plaque?
Mathematics
1 answer:
Svetllana [295]3 years ago
3 0

Answer:

The perimeter of the plaque is 28 inches.

Step-by-step explanation:

Given : A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches. The perpendicular distance from a side to the center is 5 inches to the nearest inch.

To find : What is the perimeter of the plaque?

Solution :

The 7-sided polygon can be divided into seven triangles whose height, h is equal to the perpendicular distance from each side to the center.

The base of each triangle is equal to the length of a side, s.

The area of each triangle is A=\frac{1}{2}\times s\times h

The area of the whole polygon is A_p=\frac{1}{2}\times 7s\times h

Now, the perimeter of a regular 7-sided polygon is P=7s.

Substitute in area,

A_p=\frac{1}{2}\times P\times h

We have given, A_p=70\ in^2 and h=5\ in

70=\frac{1}{2}\times P\times 5

P=\frac{70\times 2}{5}

P=28

The perimeter of the plaque is 28 inches.

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