Question

A square-based prism has a base area of 64 square meters and a total surface area of 272 square meters. What is the height of the prism?

Answer 1

4.5 m

Explanation:

-Let a be the base lengths and h be the height, the surface area can be calculated as:

`A=2a^2+4ah`

Where
`2a^2` is the base are:

#Substitute the known values in the formula to solve for h:

`2a^2=64* 2\\a^2=64\\\\a=8\\\\\therefore A=2a^2+4ah\\272=2* 64+4* 8h\\\\144=32h\\\\h=4.5`

Hence, the prism's height is 4.5 m