Question

A right prism has height 8 and triangular bases with sides of length 7, 8, and 9. What is the:
a) Volume of the prism?
b) Total surface area of the prism?

Answer 1

use Heron's Formula to find the area of the base

Answer 2

Or, find ∠C using the law of cosines. If the sides are a,b,c opposite ∠s A,B,C, and c=9, then
9^2 = 7^2 + 8^2 - 2*7*8*cosC
Now the area of the base is 1/2 ab sinC
The faces are easy, since they are all rectangles.

Answer 3

1)
Use formula:
V=BH
First, find the perimeter:
2s=7+8+9
s=12
then find the base
b=(12(12-7)(12-8)(12-9))^1/2
=12sqrt5
-->
V=12sqrt5*8
=96sqrt5
or about 214.663 units^3

2)
Use formula:
total surface area=base perimeter*height + 2*area of base
First, find the base perimeter:
p=7+8+9=24
then find the area of base:
s=(7+8+9)/2=12
a=(12*5*4*3)^1/2=12sqrt5
-->
total surface area=24*8+2*12sqrt5
or about 245.666