Question

Here is a triangular prism

All measurements are in centimeters

Calculate the volume and surface area of the prism.

Answer 1

Volume = 42 cm^3, Surface Area = 96 cm^2

Explanation:

Volume = Area * Height

S = semi-perimeter or half of the perimeter

Area of the triangle using heron's formula =
`√(s(s-a)(s-b)(s-c))`

S = (3 + 4 + 5)/2 = 6 cm

Area of triangle =
`√(6(6-3)(6-4)(6-5))`

=
`√(6 * 3 * 2 * 1)`

=
`√(36)`

= 6 cm^2

Volume = 6 * 7

= 42 cm^3

Surface Area = Area of bases * Area of Lateral faces

Area of lateral faces = 7 * 3 + 7 * 4 + 7 * 5 = 84 cm^2

Area of bases = 6 cm^2 * 2 = 12 cm^2

Surface area = 12 cm^2 + 84 cm^2 = 96 cm^2