Geometry practice problems involving surface area, triangle area, and volume calculations.

Final Answer:
C. 186 square feet

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Explanation:
Let’s break this down step by step.

We’re finding the total surface area of a triangular prism. That means we need to add up the areas of ALL the faces — the two triangles on the ends, and the three rectangles that connect them.

Step 1: Find the area of one triangle.
The triangle has a base of 5 ft and height of 5 ft (look at the right angle symbol).
Area of a triangle = (base × height) ÷ 2
So, (5 × 5) ÷ 2 = 25 ÷ 2 = 12.5 square feet.

There are TWO triangles (one on each end), so:
12.5 × 2 = 25 square feet.

Step 2: Find the areas of the three rectangles.

- First rectangle: 5 ft by 8 ft → 5 × 8 = 40 sq ft
- Second rectangle: 7 ft by 8 ft → 7 × 8 = 56 sq ft
- Third rectangle: 8 ft by 8 ft → 8 × 8 = 64 sq ft

Add those: 40 + 56 + 64 = 160 square feet.

Step 3: Add the triangles and rectangles together.
Triangles: 25 sq ft
Rectangles: 160 sq ft
Total = 25 + 160 = 185? Wait — that’s not matching any answer!

Wait — let’s double-check the triangle.

Actually, looking again — the triangle’s base is 5 ft, but the height is also 5 ft? Yes, because there’s a right angle shown. So 12.5 × 2 = 25 is correct.

But maybe the side labeled “7 ft” is NOT the side of the triangle? Let’s look again.

Actually, the triangle sides are 5 ft, 5 ft, and 7 ft? But if it’s a right triangle with legs 5 ft and 5 ft, then the hypotenuse should be √(5²+5²) = √50 ≈ 7.07 ft — close to 7 ft. Maybe they rounded.

But in the diagram, the 7 ft is labeled on the slanted side of the triangle — which would be the hypotenuse.

So yes, triangle area is still (5×5)/2 = 12.5, times 2 = 25.

Now rectangles:

One rectangle is 5 ft by 8 ft → 40
Another is 7 ft by 8 ft → 56
Another is 8 ft by 8 ft → 64

40 + 56 + 64 = 160

25 + 160 = 185 — but that’s not an option.

Wait — maybe the triangle’s height is NOT 5 ft? Let’s read the diagram again.

Actually, the triangle has a base of 5 ft, and the height is shown as 5 ft — with the right angle mark. So it’s correct.

Hmm… maybe the side labeled “8 ft” on the bottom is actually the length of the prism? And the triangle’s sides are 5, 5, and 7.

But 5×5÷2×2 = 25

Rectangles:

- One is 5 ft (side of triangle) × 8 ft (length) = 40
- One is 7 ft (other side of triangle) × 8 ft = 56
- One is 5 ft (other side of triangle) × 8 ft = 40? Wait — no, the third side is 7 ft, not 5 ft.

Wait — the triangle has sides: 5 ft, 5 ft, and 7 ft? That doesn’t make sense for a right triangle unless it’s isosceles right triangle — but 5-5-7 isn’t right.

Actually, looking at the diagram — the triangle has a right angle between the 5 ft and 5 ft sides — so the hypotenuse is √(25+25)=√50≈7.07, which they’ve rounded to 7 ft.

So the three rectangular sides are:

- 5 ft × 8 ft = 40
- 5 ft × 8 ft = 40
- 7 ft × 8 ft = 56

Wait — that’s different! I think I misread earlier.

The triangle has two legs of 5 ft each, so the two rectangles attached to those legs are both 5 ft by 8 ft.

And the third rectangle is attached to the hypotenuse, which is 7 ft, so 7 ft by 8 ft.

So rectangles: 40 + 40 + 56 = 136

Triangles: 12.5 × 2 = 25

Total: 136 + 25 = 161

Ah! That’s option D.

But wait — the question says “total surface area”, and option D is 161.

But earlier I thought C was 186.

Let me check the options again:

A. 1,700
B. 75
C. 186
D. 161

So 161 is D.

But why did I get 185 before? Because I mistakenly used 8 ft × 8 ft for one rectangle — but that’s not correct.

The prism has three rectangular sides:

- One is 5 ft (leg) × 8 ft (length) = 40
- Another is 5 ft (other leg) × 8 ft = 40
- Third is 7 ft (hypotenuse) × 8 ft = 56

Total rectangles: 40+40+56=136

Two triangles: 12.5 each → 25

Total: 136 + 25 = 161

So the correct answer is D. 161 square feet.

I must have misread the diagram earlier.

Final Answer:
D. 161 square feet