Chapter 12.4, Problem 1ACYP

To determine

Tocalculate : The perimeter and surface area of the pentagonal prism.

Answer to Problem 1ACYP

Area of pentagonal prism $=286$ mm.2 andperimeter of pentagonal prism $=25$ mm

Explanation of Solution

Given information :

It is given that, the side(a) of the pentagonal prism = 5 mm and the height(h) = 8 mm.

Formula used : We know, thesurface area of the pentagonal prism $=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}{a}^2$ . Andperimeter of the pentagonal prism $=5\times a$ .

Calculation : Calculate the area of the pentagonal prism.

Area of the pentagonal prism $=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}{a}^2$

  $=5\times 5\times 8+\frac{1}{2}\times \sqrt{5\times (5+2\times \sqrt{5})}\times 5^2$

$=200+\frac{1}{2}\times \sqrt{5\times 9.47}\times 25$

$=200+\frac{1}{2}\times \text{6}\text{.88}\times 25$

$=200+86$

$=286$ mm.2

Now, calculate the perimeter of the pentagonal prism.

The perimeter of the pentagonal prism $=5\times a$

$=25$ mm