Surface area of rectangular prisms worksheet with diagrams and problems.

Let’s solve each problem step by step.

We are finding the surface area of rectangular prisms.
A rectangular prism has 6 faces: front/back, left/right, top/bottom.
Opposite faces are equal in size.

Formula for surface area (SA) of a rectangular prism:
> SA = 2 × (length×width + length×height + width×height)

Or you can think of it as:
> SA = 2lw + 2lh + 2wh

Where:
- l = length
- w = width
- h = height

---

Problem 1:
Dimensions: 5 cm (l), 3 cm (w), 2 cm (h)

SA = 2×(5×3 + 5×2 + 3×2)
= 2×(15 + 10 + 6)
= 2×31 = 62 cm²

---

Problem 2:
Dimensions: 20 m (l), 8 m (w), 4 m (h)

SA = 2×(20×8 + 20×4 + 8×4)
= 2×(160 + 80 + 32)
= 2×272 = 544 m²

---

Problem 3:
Dimensions: 9 ft (l), 4 ft (w), 12 ft (h)

SA = 2×(9×4 + 9×12 + 4×12)
= 2×(36 + 108 + 48)
= 2×192 = 384 ft²

---

Problem 4:
Dimensions: 7 yd (l), 4 yd (w), 3 yd (h)

SA = 2×(7×4 + 7×3 + 4×3)
= 2×(28 + 21 + 12)
= 2×61 = 122 yd²

---

Problem 5:
This is a cube! All sides = 12 in

For a cube: SA = 6 × side²
SA = 6 × 12² = 6 × 144 = 864 in²

*(Alternatively, using formula: 2×(12×12 + 12×12 + 12×12) = 2×(144+144+144)=2×432=864 — same answer)*

---

Problem 6:
Dimensions: 14 cm (l), 5 cm (w), 10 cm (h)

SA = 2×(14×5 + 14×10 + 5×10)
= 2×(70 + 140 + 50)
= 2×260 = 520 cm²

---

Problem 7:
Dimensions: 12 cm (l), 8 cm (w), 3 cm (h)

SA = 2×(12×8 + 12×3 + 8×3)
= 2×(96 + 36 + 24)
= 2×156 = 312 cm²

---

Problem 8:
Dimensions: 15 mm (l), 4 mm (w), 2 mm (h)

SA = 2×(15×4 + 15×2 + 4×2)
= 2×(60 + 30 + 8)
= 2×98 = 196 mm²

---

Problem 9:
Dimensions: 8 ft (l), 5 ft (w), 10 ft (h)

SA = 2×(8×5 + 8×10 + 5×10)
= 2×(40 + 80 + 50)
= 2×170 = 340 ft²

---

Problem 10:
Gift box: length = 20 cm, width = 14 cm, height = 10 cm

SA = 2×(20×14 + 20×10 + 14×10)
= 2×(280 + 200 + 140)
= 2×620 = 1240 cm²

So you need 1240 square centimeters of paper to wrap the gift box.

---

Final Answer:
1) 62 cm²
2) 544 m²
3) 384 ft²
4) 122 yd²
5) 864 in²
6) 520 cm²
7) 312 cm²
8) 196 mm²
9) 340 ft²
10) 1240 cm²