Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Find area of triangular bases

The base of the triangle is $5$ yd and the height is $12$ yd. Area of a triangle $A_{triangle}=\frac{1}{2}\times base\times height$. So $A_{triangle}=\frac{1}{2}\times5\times12 = 30$ yd². Since there are 2 triangular bases, the total area of the bases $A_{bases}=2\times30 = 60$ yd².

Step2: Find area of rectangular faces

There are 3 rectangular faces.
Face 1: Dimensions $11$ yd and $5$ yd, area $A_1 = 11\times5=55$ yd².
Face 2: Dimensions $11$ yd and $12$ yd, area $A_2 = 11\times12 = 132$ yd².
Face 3: Dimensions $11$ yd and $13$ yd, area $A_3 = 11\times13=143$ yd².
The total area of the rectangular faces $A_{rectangles}=55 + 132+143=330$ yd².

Step3: Calculate total surface area

The surface area of the triangular - prism $A = A_{bases}+A_{rectangles}$. So $A=60 + 330=390$ yd².

Answer:

$390$ yd²