Question

Find the surface area of the
triangular prism.
10 ft.
3 ft.
3 ft

Answer 1

Given:

The figure of a triangular prism.

To find:

The surface area of the triangular prism.

Solution:

We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.

Triangles have base 3 ft and height 2 ft.

Area of a triangle is

$Area=\dfrac{1}{2}\times base\times height$

$A_1=\dfrac{1}{2}\times (3)\times (2)$

$A_1=3$

Area of congruent triangles are congruent. So,

$A_1=A_2=3\text{ sq. units}$

Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.

Area of a rectangle is

$Area=Length\times width$

$A_3=10\times 3$

$A_3=30$

Dimensions of all three rectangles are same, therefore there areas are equal.

$A_3=A_4=A_5=30$

Now, the total surface area of the prism is

$A=A_1+A_2+A_3+A_4+A_5$

$A=3+3+30+30+30$

$A=96$

Therefore, the total surface area of the prism is 96 sq. ft.