Question

How do you figure out the surface area of this triangular prism

Answer 1

To find the surface area, there are a few things you need to do:

First, you need to find the lateral sides and base sides: I'll put in an image. The blue will be the 2 bases (triangles) and the pink will be the lateral area ( 3 rectangles)

To find the lateral area, you have to multiply the perimeter and the height:

lateral area - ph

Find the perimeter and height (perimeter will be in green and the height will be red on another image )

Perimeter is 5.2 feet (2 feet + 1 foot + 2.2 feet)

The height is 10 feet.

Multiply them both together: 5.2 • 10 = 52

The lateral area of the triangular prism is 52cm².

Now you have to the area of the 2 triangular bases:

½bh (I will put another image- the literal bases will be purple and the heights will be purple)

½(1)(2)

The area of one of the bases is 1cm². . Multiply the area of the triangle by 2 to account for both.

The area for the both bases is 2cm².

Now all you have to do is add the lateral area and 2 base areas together:


52cm² + 2cm² = 54cm².

The surface area of the triangular prism is 54cm².

Answer 2

Lateral Faces:
Area of bottom face = 1*3 = 3 sq ft
Area of left-facing face = 2*3 = 6 sq ft
Area of slanted face = 3*2.2 = 6.6 sq ft
Total Lateral Surface Area = 3+6+6.6 = 15.6 sq ft

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Base Faces:
Each base is a triangle with base 2 and height 1
Area of one base = base*height/2 = 2*1/2 = 2/2 = 1
The total base area is 2*1 = 2 sq ft

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The total surface area is therefore 15.6+2 = 17.6
I added together the total lateral surface area (15.6) and the total base area (2)

Answer: 17.6 square feet