Surface Area Worksheet 6th Grade - Free Printable

To find the surface area of each triangular prism, we need to add up the areas of all its faces.

Each prism has:
- 2 identical triangular bases (front and back)
- 3 rectangular sides (left, right, and bottom — or sometimes top, depending on orientation)

We’ll calculate each part step by step for each problem.

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Problem 1)

Given:
- Triangle base = 3 cm
- Triangle height = 2 cm → so area of one triangle = (base × height) 2 = (3 × 2) ÷ 2 = 3 cm²
→ Two triangles: 3 × 2 = 6 cm²

Rectangles:
- Top rectangle: 6 cm long × 2.5 cm wide → area = 6 × 2.5 = 15 cm²
- Bottom rectangle: same as top? Wait — looking at net: there are three rectangles.
Actually, from the net:
There’s a central rectangle that is 6 cm by 3 cm? No — let's read carefully.

Wait — in the net:
The middle vertical strip has:
- A rectangle labeled 2.5 cm high and 6 cm wide → that’s one face.
- Below it, a rectangle with height 3 cm and width 6 cm? But no — actually, the 3 cm is the base of the triangle attached to the side.

Let me reinterpret the net correctly.

In Problem 1 net:
- The two triangles are on the left and right. Each has base 3 cm and height 2 cm.
- The three rectangles are arranged vertically in the center column:
- Top rectangle: 6 cm (width) × 2.5 cm (height) → area = 15 cm²
- Middle rectangle: this is attached to the triangle’s base — so its dimensions are 6 cm (length of prism) × 3 cm (base of triangle)? But wait — the label “3 cm” is next to the triangle’s base, which is also the width of the middle rectangle.
- Actually, the middle rectangle should be 6 cm long (same as top) and 3 cm tall? But then the bottom rectangle is not labeled with height — but since the two side rectangles are identical (as per instruction), and the top is 2.5 cm, perhaps the bottom is also 2.5 cm? That doesn’t match.

Wait — re-read the problem statement:

> Each of these prisms is made from 2 isosceles triangles and 3 rectangles, two of which are identical.

So among the 3 rectangles, two are identical.

Looking at Problem 1 net:

Vertical stack of 3 rectangles:
- Top: labeled 2.5 cm (height) and 6 cm (width) → area = 6 × 2.5 = 15
- Middle: labeled 3 cm (height?) and 6 cm (width) → but 3 cm is actually the base of the triangle attached to its side — so yes, this rectangle is 6 cm by 3 cm → area = 18
- Bottom: no height given — but since two rectangles are identical, and top is 2.5, maybe bottom is also 2.5? Then middle is different.

But that would make top and bottom identical (both 6×2.5), and middle different (6×3). That fits “two of which are identical”.

Also, the triangles: each has base 3 cm and height 2 cm → area = (3×2)/2 = 3 cm² each → total for two = 6 cm²

Now rectangles:
- Top: 6 × 2.5 = 15
- Bottom: 6 × 2.5 = 15 (assuming identical to top)
- Middle: 6 × 3 = 18

Total surface area = triangles + rectangles = 6 + 15 + 15 + 18 = 54 cm²

Wait — but is the middle rectangle really 6×3? Let’s check the diagram again mentally.

In the net, the middle rectangle has the triangle attached to its left and right sides. The triangle’s base is 3 cm, so the rectangle’s width (the dimension perpendicular to the 6 cm length) must be 3 cm. Yes.

And the top and bottom rectangles are both 2.5 cm in that same direction — so they are 6 cm by 2.5 cm.

Yes. So:

Triangles: 2 × (½ × 3 × 2) = 2 × 3 = 6 cm²
Rectangles:
- Two of them: 6 × 2.5 = 15 each → 30
- One: 6 × 3 = 18
Total = 6 + 30 + 18 = 54 cm²

✔ Confirmed.

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Problem 2)

Units: inches

Net shows:
- Two triangles: each has base 6 in, height 4 in → area of one = (6×4)/2 = 12 in² → two triangles = 24 in²

Rectangles:
Three rectangles in horizontal row? Actually, looking at net:

It’s arranged with a central rectangle flanked by two others, and triangles above and below.

Central rectangle: labeled 6 in (width) and 14 in (height) → area = 6 × 14 = 84 in²

Left and right rectangles: each labeled 5 in (width) and 14 in (height) → area each = 5 × 14 = 70 in² → two of them = 140 in²

Are any two rectangles identical? Left and right are both 5×14 → yes, identical. Central is different (6×14). Fits description.

So total surface area = triangles + rectangles = 24 + 84 + 140 = 248 in²

Wait — let me double-check:

Triangles: 2 × (½ × 6 × 4) = 2 × 12 = 24 ✔️
Rectangles:
- Left: 5 × 14 = 70
- Right: 5 × 14 = 70
- Center: 6 × 14 = 84
Sum rectangles: 70+70+84 = 224
Total SA = 24 + 224 = 248 in²

✔ Correct.

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Problem 3)

Units: cm

Net:
Two triangles: each has base 10 cm, height 12 cm? Wait — look:

Triangle: base is 10 cm (labeled horizontally), and height is 12 cm (labeled vertically from base to apex). So area of one triangle = (10 × 12)/2 = 60 cm² → two triangles = 120 cm²

Rectangles:
There are three rectangles stacked vertically on the right? Or rather, in the net, we have:

From top to bottom:
- First rectangle: attached to top of triangle? Actually, the net shows:

A vertical column of three rectangles on the right? No — let's parse:

Actually, the net has:
- A triangle on the left
- Attached to its right side: a rectangle that is 10 cm wide (same as triangle base) and 13 cm tall? Labeled "13 cm" next to it.
- Below that: another rectangle, also labeled "13 cm" — so probably same size?
- And above the first rectangle? There’s a small segment labeled "10 cm" — that might be the other side.

Wait — better approach:

The prism has:
- Two triangular bases: each with base 10 cm, height 12 cm → area each = 60 cm² → total 120 cm²

The three rectangular faces correspond to the three sides of the triangle extended along the length of the prism.

What is the length of the prism? In the net, the rectangles have heights labeled 13 cm and 13 cm — so likely the prism length is 13 cm.

The triangle is isosceles with base 10 cm and height 12 cm. We can find the equal sides using Pythagoras.

Half-base = 5 cm, height = 12 cm → so each equal side = (5² + 12²) = √(25 + 144) = √169 = 13 cm.

Oh! So the triangle has sides: 10 cm (base), and two sides of 13 cm each.

Therefore, the three rectangular faces are:
- One rectangle: 10 cm (base) × 13 cm (prism length) → area = 130 cm²
- Two rectangles: each 13 cm (side) × 13 cm (length) → area each = 169 cm² → total 338 cm²

But wait — in the net, we see two rectangles labeled 13 cm — that matches the two 13×13 rectangles? But 13×13 is square, but here it’s rectangle with sides 13 and 13 — yes.

But let’s confirm with the net drawing:

In Problem 3 net:
- There is a triangle on the left with base 10 cm and height 12 cm.
- Attached to the right of the triangle is a rectangle that is 10 cm wide and... what height? The label "13 cm" is written beside a vertical rectangle below it? Actually, looking:

The net shows:
- A vertical stack of two rectangles on the right, each labeled "13 cm" — meaning their height is 13 cm.
- Above them, there’s a horizontal segment labeled "10 cm" — that’s the top of the upper rectangle?
- Also, the triangle is attached to the left of the middle of this stack?

Actually, standard interpretation: the three rectangles correspond to the three sides of the triangle, each multiplied by the prism length.

Since the triangle sides are 10 cm, 13 cm, 13 cm, and the prism length is 13 cm (from the labels on the rectangles), then:

Rectangle areas:
- 10 × 13 = 130
- 13 × 13 = 169
- 13 × 13 = 169

Total rectangles = 130 + 169 + 169 = 468 cm²

Triangles = 2 × (½ × 10 × 12) = 120 cm²

Total SA = 120 + 468 = 588 cm²

But let’s verify with the net labels:

In the net, we see:
- Two rectangles explicitly labeled "13 cm" — likely their height is 13 cm.
- The width of those rectangles: one is attached to the triangle’s side — which we calculated as 13 cm, so 13×13.
- The other rectangle: the one between the triangles? It has width 10 cm (same as triangle base) and height 13 cm? But in the net, there’s a label "10 cm" near the top — possibly indicating the width of the top rectangle.

Actually, looking again: the net has a central vertical strip consisting of three parts:
- Top: a rectangle with width 10 cm (labeled) and height ?
- Middle: a rectangle with height 13 cm (labeled) and width ?
- Bottom: a rectangle with height 13 cm (labeled) and width ?

This is confusing. Alternative approach: since the triangle is isosceles with base 10 and height 12, the equal sides are 13, as calculated.

The prism’s length (distance between the two triangular bases) is given by the dimension of the rectangles perpendicular to the triangle sides. In the net, the rectangles that are not the "base" rectangle are labeled 13 cm — which matches the side length, suggesting that the prism length is 13 cm.

Moreover, in the net, the two rectangles labeled "13 cm" are likely the ones corresponding to the 13 cm sides of the triangle, so their area is 13 cm (side) × 13 cm (length) = 169 each.

The third rectangle corresponds to the base of the triangle: 10 cm × 13 cm = 130.

And the two triangles: 120 total.

So yes, 120 + 130 + 169 + 169 = 588 cm².

✔ Confirmed.

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Problem 4)

Units: cm

Net:
Two triangles: each has base 12 cm, height 8 cm → area of one = (12 × 8)/2 = 48 cm² → two triangles = 96 cm²

Rectangles:
Three rectangles. From the net:

There is a central rectangle labeled 12 cm (width) and ? height — but adjacent to it are two other rectangles.

Labels:
- Left rectangle: 15 cm (height) and 10 cm (width) → area = 15 × 10 = 150 cm²
- Central rectangle: 12 cm (width) and ? — but the height should be the same as the left rectangle if they share the same edge? Actually, in the net, the central rectangle is between the two triangles, and its height is the same as the prism length.

Wait — the triangle has base 12 cm, and we need the other two sides.

Triangle: base 12 cm, height 8 cm → half-base = 6 cm → so each equal side = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

So the triangle has sides: 12 cm (base), and two sides of 10 cm each.

Prism length: from the net, the rectangles have a dimension of 15 cm — labeled on the left rectangle as height, and likely the same for others.

So the three rectangular faces are:
- Base rectangle: 12 cm × 15 cm = 180 cm²
- Two side rectangles: each 10 cm × 15 cm = 150 cm² each → total 300 cm²

Total rectangles = 180 + 300 = 480 cm²

Triangles = 96 cm²

Total SA = 96 + 480 = 576 cm²

Check with net:

Left rectangle: labeled 15 cm and 10 cm → 15×10=150 → this is one side rectangle (10 cm side of triangle × 15 cm length)

Central rectangle: should be 12 cm (base) × 15 cm = 180 — but in the net, it’s not labeled with height, but since it’s connected, height is 15 cm.

Right rectangle: should be same as left — 10 cm × 15 cm = 150 — and in the net, it’s symmetric, so yes.

Triangles: 2 × (½ × 12 × 8) = 96

Total: 150 + 180 + 150 + 96 = 576 cm²

✔ Correct.

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Final Answers:

1) 54 cm²
2) 248 in²
3) 588 cm²
4) 576 cm²

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Final Answer:
1) 54 cm²
2) 248 in²
3) 588 cm²
4) 576 cm²