Respuesta :
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 [tex]A=\frac{1}{2}\times s\times h[/tex]
The area of the whole polygon is [tex]A_p=\frac{1}{2}\times 7s\times h[/tex]
Now, the perimeter of a regular 7-sided polygon is [tex]P=7s[/tex].
Substitute in area,
[tex]A_p=\frac{1}{2}\times P\times h[/tex]
We have given, [tex]A_p=70\ in^2 and h=5\ in[/tex]
[tex]70=\frac{1}{2}\times P\times 5[/tex]
[tex]P=\frac{70\times 2}{5}[/tex]
[tex]P=28[/tex]
The perimeter of the plaque is 28 inches.
