Aside length of the base is 6 inches, and the apothem of the base is 4 inches. the height of the prism is 18 inches. what is the area of a cross-section of the prism? what is the volume of the prism?
a) 12 in2; 216 in3 b) 24 in2; 432 in3 c) 60 in2; 1080 in3
d) 120 in2; 2160 in3

Area and volume of pentagonal prism is 660 inches² and 1080 inches³

Step-by-step explanation:

Given : A pentagonal prism having  side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches.

We have to calculate

1) area of a cross-section of the prism

2) the volume of the prism

1) Area of cross section of pentagonal prism =5ab +5bh

Where a = apothem

b - base length

h = height.

For the given pentagon

apothem = 4 inches

base = 6 inches

Height = 18 inches

Area of cross section of pentagonal prism =5 ×4 × 6 + 5× 6 × 18

Area of cross section of pentagonal prism = 120 + 540

Area of cross section of pentagonal prism = 660 inches²

2) Volume of pentagonal prism =

Where, A = apothem

P is perimeter of base

H= height

Perimeter of pentagon is 5b = 30 inches

Volume of pentagonal prism =

Volume of pentagonal prism = 1080 inches³

Thus, Area and volume of pentagonal prism is 660 inches² and 1080 inches³.

its a straight line parallel to the time axis

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.