Question

A triangular prism has a triangular base with dimensions of 3" by 4" by 5"

and a volume of 210 in? What is the surface area of the triangular prism?​

Answer 1

432in²

Explanation:

Volume of a triangular based prism =
`Base\ area * height`

Base area = Area of the triangle = 1/2 * base of the triangle * height of the triangle

Since the triangular base has dimensions of 3" by 4" by 5", then it is a right angled triangle with base of 4in and height of 3in

Base Area = 1/2 * 3 * 4

Base Area = 6in²

Substituting the volume and the base area value in the formula to get the height of the prism we have;

210 = 6H

H = 210/6

H = 35in

Surface area of the triangular prism = bh + pH

b= base of the triangle = 4in

h- height of the triangle = 3in

p= perimeter of the triangle = 3+4+5 = 12in

H= height of the prism = 35in

Surface area of the triangular prism = 4(3)+12(35)

Surface area of the triangular prism = 12+420in

Surface area of the triangular prism = 432in²