To find the surface area of a rectangular prism, we need to calculate the area of all six faces and add them together.
The formula for the surface area is:
Surface Area = 2(length × width) + 2(length × height) + 2(width × height)
Or simply:
$2(lw + lh + wh)$
Here are the step-by-step solutions for each problem:
1) Dimensions: $l=13$, $w=9$, $h=3$ (mm)
* Top/Bottom: $13 \times 9 = 117$
* Front/Back: $13 \times 3 = 39$
* Sides: $9 \times 3 = 27$
* Sum: $117 + 39 + 27 = 183$
* Multiply by 2: $183 \times 2 = 366$
*
Answer: $366 \text{ mm}^2$
2) Dimensions: $l=20$, $w=4$, $h=6$ (cm)
* Top/Bottom: $20 \times 4 = 80$
* Front/Back: $20 \times 6 = 120$
* Sides: $4 \times 6 = 24$
* Sum: $80 + 120 + 24 = 224$
* Multiply by 2: $224 \times 2 = 448$
*
Answer: $448 \text{ cm}^2$
3) Dimensions: $l=14$, $w=5$, $h=8$ (m)
* Top/Bottom: $14 \times 5 = 70$
* Front/Back: $14 \times 8 = 112$
* Sides: $5 \times 8 = 40$
* Sum: $70 + 112 + 40 = 222$
* Multiply by 2: $222 \times 2 = 444$
*
Answer: $444 \text{ m}^2$
4) Dimensions: $l=17$, $w=4$, $h=14$ (ft)
* Top/Bottom: $17 \times 4 = 68$
* Front/Back: $17 \times 14 = 238$
* Sides: $4 \times 14 = 56$
* Sum: $68 + 238 + 56 = 362$
* Multiply by 2: $362 \times 2 = 724$
*
Answer: $724 \text{ ft}^2$
5) Dimensions: $l=13$, $w=4$, $h=9$ (in)
* Top/Bottom: $13 \times 4 = 52$
* Front/Back: $13 \times 9 = 117$
* Sides: $4 \times 9 = 36$
* Sum: $52 + 117 + 36 = 205$
* Multiply by 2: $205 \times 2 = 410$
*
Answer: $410 \text{ in}^2$
6) Dimensions: $l=14$, $w=8$, $h=9$ (mm)
* Top/Bottom: $14 \times 8 = 112$
* Front/Back: $14 \times 9 = 126$
* Sides: $8 \times 9 = 72$
* Sum: $112 + 126 + 72 = 310$
* Multiply by 2: $310 \times 2 = 620$
*
Answer: $620 \text{ mm}^2$
7) Dimensions: $l=12$, $w=4$, $h=7$ (cm)
* Top/Bottom: $12 \times 4 = 48$
* Front/Back: $12 \times 7 = 84$
* Sides: $4 \times 7 = 28$
* Sum: $48 + 84 + 28 = 160$
* Multiply by 2: $160 \times 2 = 320$
*
Answer: $320 \text{ cm}^2$
8) Dimensions: $l=19$, $w=6$, $h=4$ (in)
* Top/Bottom: $19 \times 6 = 114$
* Front/Back: $19 \times 4 = 76$
* Sides: $6 \times 4 = 24$
* Sum: $114 + 76 + 24 = 214$
* Multiply by 2: $214 \times 2 = 428$
*
Answer: $428 \text{ in}^2$
9) Dimensions: $l=8$, $w=4$, $h=15$ (ft)
* Top/Bottom: $8 \times 4 = 32$
* Front/Back: $8 \times 15 = 120$
* Sides: $4 \times 15 = 60$
* Sum: $32 + 120 + 60 = 212$
* Multiply by 2: $212 \times 2 = 424$
*
Answer: $424 \text{ ft}^2$
10) Gift Box: $l=20$, $w=14$, $h=10$ (cm)
* Top/Bottom: $20 \times 14 = 280$
* Front/Back: $20 \times 10 = 200$
* Sides: $14 \times 10 = 140$
* Sum: $280 + 200 + 140 = 620$
* Multiply by 2: $620 \times 2 = 1240$
*
Answer: $1240 \text{ cm}^2$
Final Answer:
1) 366 mm²
2) 448 cm²
3) 444 m²
4) 724 ft²
5) 410 in²
6) 620 mm²
7) 320 cm²
8) 428 in²
9) 424 ft²
10) 1240 cm²
Parent Tip: Review the logic above to help your child master the concept of volume surface area worksheet.
