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PSYCHO15rus [73]
3 years ago
9

WILL GIVE THE BRAINLEST Find the surface area of the triangular prism​

Mathematics
1 answer:
OLEGan [10]3 years ago
3 0

Answer:

<h2>Surface Area =  267 in²   </h2><h2>V = 162 in³</h2>

Step-by-step explanation:

The surface area consists of 3 rectangles of the sides, and the two base triangles.

The front rectangle has dimensions of 12x9, so it's area is 108 in²

The back rectangle has dimensions of 7x12, so it's are is 84 in²

The side rectangle has dimensions of 4x12, so it's area is 48 in²

The top and bottom triangles have a base of 9 and a height of 3, so their area is

A = (1/2)(9)(3) = 27/2, but there are 2 of them, so their combined area is (27/2)(2) = 27 in²

The total surface area is 108 + 84 + 48 + 27 = 267 in²

The formula for volume of a triangular prism is

V = (1/2)bhd    where b is the base of the base triangle, h is the height of the base triangle, and d is the depth of prism.

We have b = 9, h = 3, and d = 12, so the volume is

V = (1/2)(9)(3)(12)

 

   V = (1/2)(27)(12)

           V = (1/2)(324)

<h2>                 V = 162 in³</h2>
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