Question

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?

Answer 1

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.