Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer. 20 m 12 m 18 m 16 m

Explanation:

Step1: Find area of triangular bases

The base triangle has base $b = 16$ m and height $h=12$ m. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$. So $A_{triangle}=\frac{1}{2}\times16\times12 = 96$ m². Since there are 2 triangular bases, the total area of the bases is $2\times96=192$ m².

Step2: Find area of rectangular faces

There are 3 rectangular faces.
Face 1: With dimensions 18 m and 16 m, area $A_1 = 18\times16=288$ m².
Face 2: With dimensions 18 m and 12 m, area $A_2 = 18\times12 = 216$ m².
Face 3: With dimensions 18 m and 20 m, area $A_3=18\times20 = 360$ m².
The total area of rectangular faces is $A_{rect}=288 + 216+360=864$ m².

Step3: Calculate total surface area

The surface area $A$ of the triangular - prism is the sum of the area of the bases and the area of the rectangular faces. So $A=192 + 864=1056$ m².

Answer:

$1056$ m²