Question

An aerial map shows the Pentagon. On the map, it covers 608.7 square inches and the distance from the center of the Pentagon to a vertex is16 inches. How long is each side of the Pentagon on the map?16 inThe apothem of the Pentagon is about inches long. The area of a regular pentagon is equal to its perimeter times its apothemdivided byV. Therefore, the perimeter of the Pentagon on the map is about inches. So, each side is aboutinches long on the map.

Answer 1

Answer: The apothem of the Pentagon is about 12.9 inches long. The area of a regular pentagon is equal to its perimeter times its apothem divided by 2. Therefore, the perimeter of the Pentagon on the map is about 94.4 inches. So, each side is about 18.9 inches long on the map.

Answer 2

Area = 608.7 in2

Area = ( perimeter x apothem)/2

radius = 16 in

a = apothem = r x cos 180/n

Where n is the number of sides (5)

a = 16 x cos 180/5 = 12.9

The area of a regular pentagon is equal to its perimeter times its apothem divided by 2.

Area = ( perimeter x apothem )/2

608.7 = (p x 12.9 ) / 2

2 (608.7 ) = p x 12.9

1217.4 = 12.9p

1217.4/12.9 = p

p= 94.4

permieter = 94.4

For the side apply:

`a=(S)/(2\tan ((180)/(n)))`
`12.9=\frac{S}{2\text{tan}((180)/(5))}`
`12.9\cdot(2\tan 36)=S`

S = side lenght = 18.9

Answers:

apothem = 12.9

2

perimeter = 94.4

side = 18.9