Finding Surface Area Using Nets #2 | Worksheet - Free Printable

Let’s solve each problem one by one. We’ll find the surface area of each 3D shape using its net. The net shows all the faces laid out flat, so we just need to calculate the area of each face and add them up.

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Problem 1: Cube (all sides 3 yd)

A cube has 6 identical square faces.

Each face is a square with side = 3 yd
Area of one face = 3 × 3 = 9 sq yd
Total surface area = 6 × 9 = 54 sq yd

✔ Check: All edges are equal → it’s a cube → 6 same squares → correct.

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Problem 2: Rectangular Prism (7 cm × 4 cm × 6 cm)

This prism has 3 pairs of identical rectangles:

- Two faces: 7 cm × 4 cm → Area = 28 cm² each → total for pair = 56 cm²
- Two faces: 7 cm × 6 cm → Area = 42 cm² each → total for pair = 84 cm²
- Two faces: 4 cm × 6 cm → Area = 24 cm² each → total for pair = 48 cm²

Add them: 56 + 84 + 48 = 188 cm²

✔ Check: Net shows 6 rectangles — 2 of each size → matches our calculation.

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Problem 3: Triangular Prism

The net shows:
- Two triangular bases
- Three rectangular sides

First, triangles:
Base = 6 m, Height = 8 m (from diagram)
Area of one triangle = (1/2) × base × height = (1/2) × 6 × 8 = 24 m²
Two triangles → 2 × 24 = 48 m²

Now rectangles:
From net, we see three rectangles:
- One is 10 m × 13 m? Wait — let’s look carefully.

Actually, from the 3D drawing and net:
The triangular base has sides: 6 m, 8 m, and 10 m (since 6-8-10 is a right triangle).

The prism length (depth) is 13 m? Wait — no, looking at the net:

In the net, the large rectangle in the middle is divided into three parts:
- Left rectangle: width = 6 m, height = 10 m? Hmm — better to match labels.

Looking again:

In the 3D figure:
- Triangle base: 6 m, height 8 m, hypotenuse 10 m (right triangle)
- The prism extends 13 m deep? But in the net, the long rectangle is labeled 13 m on top, and below it says “10 m” and “8 m”.

Wait — actually, in the net:

There are three rectangles attached to the triangles:
- One rectangle: 6 m wide × 10 m tall? No — let’s read dimensions from net.

Net shows:
- Bottom triangle: base 6 m, height 8 m
- Attached rectangles:
- Left rectangle: height 10 m, width ? — actually, the vertical dimension of the big rectangle is 10 m + 8 m + something? This is messy.

Alternative approach: From the 3D sketch:

It’s a triangular prism with:
- Triangular ends: base 6 m, height 8 m → area per triangle = 24 m² → two = 48 m²
- Three rectangular faces:
- Rectangle 1: 6 m (base) × 13 m (length of prism) → 78 m²
- Rectangle 2: 8 m (height) × 13 m → 104 m²
- Rectangle 3: 10 m (hypotenuse) × 13 m → 130 m²

Wait — but in the net, the long rectangle is shown as having height 10 m + 8 m + ...? Actually, looking at the net image description:

The net has:
- A central strip of three rectangles stacked vertically: heights 10 m, 8 m, and then another? And width 13 m? Then triangles on left and right.

Actually, standard triangular prism net: two triangles and three rectangles.

Given the 3D drawing labels:
- Triangle: legs 6 m and 8 m, hypotenuse 10 m
- Prism length (the distance between triangles) is 13 m? But in the net, the rectangle next to the triangle is labeled 13 m on top, and the side is 10 m? I think there's confusion.

Wait — re-examining the user’s image description:

For problem 3:
3D shape: triangular prism with:
- Base triangle: 6 m (base), 8 m (height), 10 m (side)
- The "length" of the prism (how far it goes back) is 13 m? But in the net, the big rectangle is 13 m wide and has sections of 10 m, 8 m, and... wait, the net shows a rectangle that is 13 m wide and total height 10+8=18? That doesn’t make sense.

Actually, looking at common problems like this:

Often, the triangular prism has:
- Triangles: base 6, height 8 → area 24 each → 48 total
- Rectangles:
- 6 × 10 = 60? No.

I think I misread. Let me try again based on typical labeling.

In many textbooks, for such a net:

The three rectangles correspond to the three sides of the triangle times the length of the prism.

From the 3D drawing:
- The triangle has sides 6 m, 8 m, 10 m
- The prism length (the edge perpendicular to the triangle) is 13 m? But in the net, the rectangle attached to the 6m side is 6x13, etc.

But in the net provided, it shows:

A central column of three rectangles:
- Top rectangle: 13 m wide, 10 m high
- Middle rectangle: 13 m wide, 8 m high
- Bottom rectangle: 13 m wide, ? — wait, it might be 6 m? But not labeled.

Actually, looking back at the original problem statement in the image:

For problem 3, the 3D shape has:
- Triangle with base 6 m, height 8 m, and slant side 10 m
- The depth (prism length) is 13 m? But in the net, the large rectangle is labeled 13 m on top, and on the side it has 10 m and 8 m marked.

Perhaps the 13 m is the length of the prism, and the rectangles are:
- 6 m × 13 m
- 8 m × 13 m
- 10 m × 13 m

That makes sense because the triangle sides are 6,8,10.

So areas:
- Rect1: 6×13 = 78
- Rect2: 8×13 = 104
- Rect3: 10×13 = 130
Sum of rectangles = 78+104+130 = 312
Plus two triangles: 2×(0.5×6×8) = 2×24 = 48
Total = 312 + 48 = 360 m²

But let’s verify with the net description: the net shows a big rectangle that is 13 m wide and has heights adding to 10+8+6? 24 m? But in the image, it might be drawn differently.

Another way: in some nets, the three rectangles are arranged in a row, but here it seems stacked.

Given the labels in the net: it says "13 m" on top of the big rectangle, and on the left side of the triangles, it has "10 m", "8 m", "6 m" — probably indicating the heights of the rectangles.

Actually, upon second thought, in the net for problem 3, the central part is a single rectangle that is 13 m wide and (10 + 8 + 6) m tall? 24 m? But that would be unusual.

I recall that in some diagrams, the net for a triangular prism has the three rectangles side by side, but here it might be stacked.

To resolve this, let's assume the standard interpretation:

The triangular prism has:
- Two triangular faces: each with area (1/2)*6*8 = 24 → total 48
- Three rectangular faces: each corresponding to a side of the triangle times the length of the prism.

What is the length of the prism? In the 3D drawing, the edge going back is labeled 13 m? Or is it 10 m?

Looking at the user's input: for problem 3, the 3D shape has "10 m" on the slant, "8 m" height, "6 m" base, and then "13 m" on the top edge of the prism — likely the length.

In the net, the large rectangle is 13 m wide, and the heights of the three sections are 10 m, 8 m, and 6 m — which correspond to the three sides of the triangle.

Yes! So the three rectangles are:
- 13 m × 10 m = 130
- 13 m × 8 m = 104
- 13 m × 6 m = 78
Sum = 130+104+78 = 312
Triangles: 2 * (0.5*6*8) = 48
Total = 312 + 48 = 360 m²

✔ Confirmed.

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Problem 4: Square Pyramid

Net shows:
- One square base
- Four triangular faces

From 3D drawing:
- Base is square: 10 in × 10 in → area = 100 in²
- Each triangular face: base 10 in, height 9 in (slant height)

Area of one triangle = (1/2) × base × height = (1/2) × 10 × 9 = 45 in²
Four triangles = 4 × 45 = 180 in²

Total surface area = base + lateral = 100 + 180 = 280 in²

✔ Check: Net shows one square and four triangles — matches.

Note: The 10 in on the pyramid is the base edge, and 9 in is the slant height of the triangle — correct for surface area.

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Final Answers:

1. 54 sq yd
2. 188 sq cm
3. 360 sq m
4. 280 sq in

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Final Answer:
1. 54
2. 188
3. 360
4. 280