Question

The right triangular prism and its dimensions are shown below. What is the total surface area, in square inches, of the right triangular prism?

Answer 1

Answer:

a) 84 in²

Step-by-step explanation:

So we need to find the surface are of each of the 5 sides

Lets start with the top slanted portion of the prism

• The surface area of a rectangle is A = b×h

• Here the base is 6 and the height is 5, so plugging these into our formula we get A = (6)(5) = 30 in²

Now we can move onto the base of the prism

• This shape is also a rectangle so we will use the same formula A = b×h
• Here the base is 6 and the height is 4, so plugging these into our formula we get A = (6)(4) = 24 in²

We will move to the back of the prism

• This is the last and final rectangle of the figure and we will use the same formula as before, A = b×h
• Here the base is 6 and the height is 3, so plugging these into our formula we get A = (6)(3) = 18 in²

Now we can go to the sides of the prism, the triangles

• Since the triangles are the same size on both sides we only need to find the surface area of one of them and make sure to add it twice when finding the surface area of the whole figure
• The surface area of a triangle is half that of a rectangle because a triangle is half of a rectangle/square: A = $\frac{1}{2}$ b×h
• Here the base is 4 and the height is 3, so plugging these into our formula we get A = $\frac{1}{2}$(4)(3) = $\frac{1}{2}$(12) = 6 in²

Now we can add together all of the surface areas we calculated:

30 in² + 24 in² + 18 in² + 6 in² + 6 in² = 84 in²

Answer 2

Surface area of given prism is 84 inch², so option 'A' is the correct answer to the following question.

Surface area of rectangle and triangle:

Surface area of given prism = 2[Surface area of triangle] + 3[Surface area of rectangle]

Surface area of given prism = 2[(1/2)(b)(h)] + 3[(l)(b)]

Surface area of given prism = 2[(1/2)(3)(4)] + 3[(4)(6)]

Surface area of given prism = 2[(1/2)(12)] + 3[(24)]

Surface area of given prism = 12 + 72

Surface area of given prism = 84 inch²

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