This worksheet provides nine practice problems for calculating the surface area of various prisms and cylinders using given dimensions.

Let’s solve each shape one by one. We’ll use π = 3.14 as instructed.

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Shape a: Triangular Prism (base is triangle, sides are rectangles)
Given:
- Triangle base = 8 ft, height = 6 ft → area of triangle = (1/2)*8*6 = 24 ft²
- There are two triangular bases → 2 * 24 = 48 ft²
- Three rectangular faces:
- One rectangle: 8 ft × 10 ft = 80 ft²
- Two other rectangles: each is hypotenuse side × length. First find hypotenuse: √(6² + 8²) = √(36+64) = √100 = 10 ft → so both side rectangles are 10 ft × 10 ft = 100 ft² each? Wait — no! The prism length is 10 ft, and the three sides of the triangle are 6, 8, and 10. So the three rectangles are:
- 6 ft × 10 ft = 60 ft²
- 8 ft × 10 ft = 80 ft²
- 10 ft × 10 ft = 100 ft²
→ Total lateral surface area = 60 + 80 + 100 = 240 ft²
→ Total SA = 48 + 240 = 288 ft²

Wait — let me double-check:
Triangle area: (1/2)*8*6 = 24 → two triangles: 48
Rectangles: perimeter of triangle times length? Perimeter = 6+8+10=24 → 24×10=240 → yes.
Total: 48 + 240 = 288 ft²

✔ Shape a: 288 ft²

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Shape b: Square Pyramid
Base: square 5 m × 5 m → area = 25 m²
Four triangular faces: each has base 5 m, slant height 7 m → area of one triangle = (1/2)*5*7 = 17.5 m²
Four triangles: 4 * 17.5 = 70 m²
Total SA = base + lateral = 25 + 70 = 95 m²

Note: In pyramids, sometimes “surface area” includes only lateral, but here it says “each shape”, and for prisms/cylinders we include all surfaces. For pyramid, typically total SA includes base unless specified otherwise. Since problem doesn’t say “lateral”, we include base.

✔ Shape b: 95 m²

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Shape c: Rectangular Prism
Dimensions: 12 in × 5 in × 4 in
SA = 2(lw + lh + wh) = 2(12*5 + 12*4 + 5*4) = 2(60 + 48 + 20) = 2(128) = 256 in²

✔ Shape c: 256 in²

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Shape d: Rectangular Prism
Dimensions: 9 cm × 5 cm × 3 cm
SA = 2(9*5 + 9*3 + 5*3) = 2(45 + 27 + 15) = 2(87) = 174 cm²

✔ Shape d: 174 cm²

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Shape e: Triangular Prism
Triangle base: 12 yd, height: 5 yd → area = (1/2)*12*5 = 30 yd² → two triangles: 60 yd²
Sides of triangle: 5, 12, and hypotenuse = √(5²+12²)=√(25+144)=√169=13 yd
Prism length = 20 yd
Lateral SA = perimeter × length = (5+12+13)*20 = 30*20 = 600 yd²
Total SA = 60 + 600 = 660 yd²

✔ Shape e: 660 yd²

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Shape f: Cylinder
Radius r = 6 in, height h = 10 in
SA = 2πr² + 2πrh = 2πr(r + h)
= 2 * 3.14 * 6 * (6 + 10)
= 2 * 3.14 * 6 * 16
First: 2*6=12; 12*16=192; 192*3.14
Calculate: 192 * 3 = 576; 192 * 0.14 = 26.88 → total = 576 + 26.88 = 602.88 in²

✔ Shape f: 602.88 in²

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Shape g: Cylinder
Diameter = 18 ft → radius r = 9 ft, height h = 12 ft
SA = 2πr(r + h) = 2 * 3.14 * 9 * (9 + 12) = 2 * 3.14 * 9 * 21
Step: 2*9=18; 18*21=378; 378*3.14
378 * 3 = 1134; 378 * 0.14 = 52.92 → total = 1134 + 52.92 = 1186.92 ft²

✔ Shape g: 1186.92 ft²

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Shape h: Rectangular Prism (tilted, but dimensions given)
Dimensions: 10 ft × 6 ft × 4 ft
SA = 2(10*6 + 10*4 + 6*4) = 2(60 + 40 + 24) = 2(124) = 248 ft²

✔ Shape h: 248 ft²

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Shape i: Cube
Side = 12 in
SA = 6 * s² = 6 * 144 = 864 in²

✔ Shape i: 864 in²

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Final Answers:

a) 288 ft²
b) 95 m²
c) 256 in²
d) 174 cm²
e) 660 yd²
f) 602.88 in²
g) 1186.92 ft²
h) 248 ft²
i) 864 in²

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Final Answer:
a) 288 ft²
b) 95 m²
c) 256 in²
d) 174 cm²
e) 660 yd²
f) 602.88 in²
g) 1186.92 ft²
h) 248 ft²
i) 864 in²