Chapter 12.4, Problem 1BCYP

To determine

Tocalculate : The perimeter and surface area of the triangular prism and round to nearest tenth.

Answer to Problem 1BCYP

Area of prism= $468$ ft², and perimeter of prism $=36$ ft.

Explanation of Solution

Given information :

In thistriangular prism, a = 9 ft. h = 10 ft. b = 15 ft.

Formula used : To find the area of a triangular prism, we will use the surface area of the triangular prism $=2\times \frac{1}{2}\left(a\times c\right)+\left(h\times c\right)+\left(a\times h\right)+\left(h\times b\right)$ . And for finding c, we will usethe Pythagoras theorem, $c=\sqrt{b^2-a^2}$ . And to find the perimeter of the prism, we will add up all the sides.

Calculation : Calculate the area of the triangular prism.

To find the area of a triangular prism, we will have to find perpendicular.

c = $\sqrt{h^2-b^2}$

$=\sqrt{{15}^2-9^2}$

= $\sqrt{144}$

= $12$ ft.

Area of the triangular prism $=2\times \frac{1}{2}\left(a\times c\right)+\left(h\times c\right)+\left(a\times h\right)+\left(h\times b\right)$

$=108+120+90+150$

$=468$ ft.2

Now, calculate the perimeter of the prism.

Perimeter $=Sumofallsides$

$=a+c+b$

$=9+12+15$

$=36$ ft.