Question

A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13 What is the: Total Surface Area of the Prism

Answer 1

Given:

A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.

To find:

The total surface area of the prism.

Solution:

We have,

Height of prism = 7½ = 7.5

Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because

`5^2+12^2=13^2`

`25+144=169`

`169=169`

So, the base of the prism is a right triangle.

Area of a triangle is

`Area=(1)/(2)* base * height`

`A_1=(1)/(2)* 5* 12`

`A_1=30`

The area of the base is equal to the area of the top, i.e.,
`A_2=30` sq units.

Perimeter of the base is

`P=5+12+13`

`P=30`

The curved surface area of the prism is

`CSA=\text{Perimeter of the base}* \text{Height of the prism}`

`CSA=30* 7.5`

`CSA=225`

Now, the total area of the prism is

`A=A_1+A_2+CSA`

`A=30+30+225`

`A=285`

Therefore, the total surface area of the triangular prism is 285 square units.