Question

Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6in. The height of the prism is 10in

Answer 1

ANSWER

$211.2 {in}^{2}$

EXPLANATION

The surface area of a triangular prism is

equal to the area of two triangular faces

plus the area of the three rectangular faces.

The area of the equilateral triangle is calculated using the formula:

$= 2 \times \frac{ \sqrt{3} }{4} {s}^{2} + 3 \times \: bh$

where s=6 is the length of one side.

and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.

Surface area

$= 2 \times \frac{ \sqrt{3} }{4} \times {6}^{2} + 3 \times \: 6 \times 10$

$= 18\sqrt{3} + 180$

=211.2square inches.