Answer:
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 = \(\frac{AP}{2} \times H\)
Where, A = apothem
P is perimeter of base
H= height
Perimeter of pentagon is 5b = 30 inches
Volume of pentagonal prism = \(\frac{4\times 30}{2} \times 18\)
Volume of pentagonal prism = 1080 inches³
Thus, Area and volume of pentagonal prism is 660 inches² and 1080 inches³.
