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
So, the base of the prism is a right triangle.
Area of a triangle is
The area of the base is equal to the area of the top, i.e., sq units.
Perimeter of the base is
The curved surface area of the prism is
Now, the total area of the prism is
Therefore, the total surface area of the triangular prism is 285 square units.