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Jet001 [13]
3 years ago
12

Can someone help me with this?

Mathematics
1 answer:
yan [13]3 years ago
4 0
I'm assuming you want the total surface area.

This is a trapezoidal prism. The bases are the parallel faces running horizontal (parallel to the ground) and they are congruent trapezoids. The lateral sides are rectangles.

-------------------------------------------------

Lateral Faces:
The back face (hidden from view) is a rectangle that is 12 inches by 3 inches, so it has an area of 12*3 = 36 sq inches

The front slant faces on the left and right are each 3*5 = 15 sq inches in area

The front center lateral face has area of 6*3 = 18 sq inches

The total lateral surface area is 15+18+15+36 = 84 sq inches

-------------------------------------------------

The bases are each the same trapezoid. The trapezoid has two parallel sides of 12 and 6 inches. Call this b1 and b2. The height of the trapezoid is h = 4. Imagine the trapezoid is laid flat in a 2D perspective instead of a 3D one.

The area of one trapezoid is...
A = h*(b1+b2)/2
A = 4*(12+6)/2
A = 4*(18)/2
A = 72/2
A = 36

So the area of both base faces combined is 2*36 = 72

-------------------------------------------------

The total surface area is then found by adding the total lateral surface area (84) and the total base area (72) to get 84+72 = 156

Final Answer: 156 square inches

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