Answer: 136 square feet
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Step-by-step explanation:
The front face is a triangle with base 6 and height 4.
The area is 0.5*base*height = 0.5*6*4 = 12 square feet
The back face is also 12 square feet since the front and back faces are identical triangles.
So far we have 12+12 = 24 square feet of surface area.
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The bottom face, that runs along the floor or ground, is a rectangle that is 6 ft by 7 ft. So we have 6*7 = 42 square feet of surface area here. This adds onto the 24 we found earlier to get 24+42 = 66 square feet so far.
To find the left and right upper faces, we'll need to find the length of the hypotenuse first. The 6 ft cuts in half to 3 ft. The right triangle on the left has side lengths of 4 ft and 3 ft as the two legs. Use the pythagorean theorem to find the hypotenuse is 5 ft. We have a 3-4-5 right triangle.
This means the upper left face is 5 ft by 7 ft leading to an area of 5*7 = 35 square feet. The same can be said about the upper right face.
So we add on 35+35 = 70 more square feet to the 66 we found earlier to get a grand total of 70+66 = 136 square feet of surface area.