Surface Area of Prisms | Worksheet - Free Printable

Explanation:
We are asked to find the surface area of each prism, then compare the two in each row and circle the one with the larger surface area.

Recall:
The surface area of a rectangular prism = 2(lw + lh + wh), where l = length, w = width, h = height.
For a triangular prism:
Surface area = (area of 2 triangular bases) + (area of 3 rectangular faces).
If the triangle is right-angled (as in the last two rows), and legs are given, area of one triangle = (1/2) × base × height.

Let’s go row by row.

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Row 1 (left prism):
Dimensions: 4 m (height), 8 m (length), 2 m (width)
Surface area = 2(lw + lh + wh) = 2(8×2 + 8×4 + 2×4)
= 2(16 + 32 + 8) = 2(56) = 112 m²

Row 1 (right prism):
Dimensions: 2 m (height), 5 m (length), 6 m (width)
Surface area = 2(5×6 + 5×2 + 6×2) = 2(30 + 10 + 12) = 2(52) = 104 m²
→ Larger: left prism (112 > 104)

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Row 2 (left prism):
Dimensions: 4 ft (height), 4 ft (length), 4 ft (width) → cube
Surface area = 6 × side² = 6 × 4² = 6 × 16 = 96 ft²

Row 2 (right prism):
Dimensions: 4 ft (height), 8 ft (length), 1 ft (width)
Surface area = 2(8×1 + 8×4 + 1×4) = 2(8 + 32 + 4) = 2(44) = 88 ft²
→ Larger: left prism (96 > 88)

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Row 3 (left prism):
Dimensions: 25 mm (height), 3 mm (width), 4 mm (length)
Surface area = 2(4×3 + 4×25 + 3×25) = 2(12 + 100 + 75) = 2(187) = 374 mm²

Row 3 (right prism):
Dimensions: 5 mm (height), 20 mm (length), 20 mm (width)
Surface area = 2(20×20 + 20×5 + 20×5) = 2(400 + 100 + 100) = 2(600) = 1200 mm²
→ Larger: right prism (1200 > 374)

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Row 4 (left triangular prism):
Triangular base: right triangle with legs 4 yd and 3 yd
→ Area of one triangle = (1/2) × 4 × 3 = 6 yd²
Two triangles: 2 × 6 = 12 yd²

Rectangular faces:
- Face 1: 4 yd × 5 yd = 20 yd²
- Face 2: 3 yd × 5 yd = 15 yd²
- Face 3: hypotenuse × 5 yd
Hypotenuse = √(4² + 3²) = √(16+9) = √25 = 5 yd
So face 3 = 5 × 5 = 25 yd²

Total surface area = 12 + 20 + 15 + 25 = 72 yd²

Row 4 (right triangular prism):
Triangular base: right triangle with legs 6 yd and 8 yd
Area of one triangle = (1/2) × 6 × 8 = 24 yd²
Two triangles: 2 × 24 = 48 yd²

Rectangular faces:
- 6 yd × 10 yd = 60 yd²
- 8 yd × 10 yd = 80 yd²
- Hypotenuse = √(6² + 8²) = √(36+64) = √100 = 10 yd
So third rectangle = 10 × 10 = 100 yd²

Total surface area = 48 + 60 + 80 + 100 = 288 yd²
→ Larger: right prism (288 > 72)

Now, for each row, we record the surface areas and identify the larger one:

Row 1: 112 m² vs 104 m² → left larger
Row 2: 96 ft² vs 88 ft² → left larger
Row 3: 374 mm² vs 1200 mm² → right larger
Row 4: 72 yd² vs 288 yd² → right larger

Since the instruction says “circle the prism with the larger surface area in that row”, the final answer should list the surface areas for each prism (as blanks to fill), and indicate which is larger — but since the question only asks us to *solve* the problem, and the format expects a Final Answer, and based on typical worksheet expectations, the expected output is likely the surface area values for each blank (in order, left to right, top to bottom).

Let’s list all 8 surface areas in order as they appear (each row has two prisms, 4 rows → 8 blanks):

1. Left Row 1: 112
2. Right Row 1: 104
3. Left Row 2: 96
4. Right Row 2: 88
5. Left Row 3: 374
6. Right Row 3: 1200
7. Left Row 4: 72
8. Right Row 4: 288

But the problem says: “Find the surface area of each prism… Then, circle the prism with the larger surface area in that row.” Since we can’t circle here, and the user just wants the solution, the correct final answer is the list of surface areas — but the instruction says: “ONLY THEN provide the final answer”, and the format expects a single boxed answer.

Wait — re-reading: The worksheet has 8 empty boxes labeled “surface area”. So the expected answer is those 8 numbers.

Thus, final answer is the eight surface areas in order:

112, 104, 96, 88, 374, 1200, 72, 288

Let me double-check all calculations:

Row 1 left: 2(8·2 + 8·4 + 2·4) = 2(16+32+8)=2·56=112 ✔
Row 1 right: 2(5·6 + 5·2 + 6·2)=2(30+10+12)=2·52=104 ✔

Row 2 left (cube 4): 6·16=96 ✔
Row 2 right: 2(8·1 + 8·4 + 1·4)=2(8+32+4)=2·44=88 ✔

Row 3 left: 2(4·3 + 4·25 + 3·25)=2(12+100+75)=2·187=374 ✔
Row 3 right: 2(20·20 + 20·5 + 20·5)=2(400+100+100)=2·600=1200 ✔

Row 4 left: triangles: 2·(0.5·4·3)=12; rects: 4·5=20, 3·5=15, 5·5=25 → 12+20+15+25=72 ✔
Row 4 right: triangles: 2·(0.5·6·8)=48; rects: 6·10=60, 8·10=80, 10·10=100 → 48+60+80+100=288 ✔

All correct.

Final Answer:
112, 104, 96, 88, 374, 1200, 72, 288