Question

surface area - rectangular prism
integers: e51
find the surface area of each rectangular prism.
1)
image of a rectangular prism with dimensions 9 in, 13 in, 3 in
surface area = ______
2)
image of a rectangular prism with dimensions 4 yd, 20 yd, 6 yd
surface area = ______
3)
image of a rectangular prism with dimensions 16 ft, 5 ft, 14 ft
surface area = ______
4)
image of a rectangular prism with dimensions 14 yd, 17 yd, 4 yd
surface area = ______
5)
image of a rectangular prism with dimensions 4 ft, 13 ft, 19 ft
surface area = ______
6)
image of a rectangular prism with dimensions 3 in, 14 in, 9 in
surface area = ______
7)
image of a rectangular prism with dimensions 3 ft, 12 ft, 2 ft
surface area = ______
8)
image of a rectangular prism with dimensions 4 in, 6 in, 13 in
surface area = ______
9)
image of a rectangular prism with dimensions 4 yd, 8 yd, 15 yd
surface area = ______

1. a rectangular - shaped box has the following dimensions: 12 yards, 8 yards, and 18 yards. what is the surface area of the box?

surface area = ______

Explanation:

The formula for the surface area (SA) of a rectangular prism is:
$$SA = 2(lw + lh + wh)$$
where $l$ = length, $w$ = width, $h$ = height

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1)

Step1: Identify dimensions

$l=13\ \text{in}, w=9\ \text{in}, h=3\ \text{in}$

Step2: Substitute into formula

$$SA = 2((13 \times 9) + (13 \times 3) + (9 \times 3))$$

Step3: Calculate inner terms

$$SA = 2(117 + 39 + 27)$$

Step4: Sum and multiply by 2

$$SA = 2(183) = 366$$

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2)

Step1: Identify dimensions

$l=20\ \text{yd}, w=6\ \text{yd}, h=4\ \text{yd}$

Step2: Substitute into formula

$$SA = 2((20 \times 6) + (20 \times 4) + (6 \times 4))$$

Step3: Calculate inner terms

$$SA = 2(120 + 80 + 24)$$

Step4: Sum and multiply by 2

$$SA = 2(224) = 448$$

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3)

Step1: Identify dimensions

$l=16\ \text{ft}, w=5\ \text{ft}, h=14\ \text{ft}$

Step2: Substitute into formula

$$SA = 2((16 \times 5) + (16 \times 14) + (5 \times 14))$$

Step3: Calculate inner terms

$$SA = 2(80 + 224 + 70)$$

Step4: Sum and multiply by 2

$$SA = 2(374) = 748$$

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4)

Step1: Identify dimensions

$l=17\ \text{yd}, w=4\ \text{yd}, h=14\ \text{yd}$

Step2: Substitute into formula

$$SA = 2((17 \times 4) + (17 \times 14) + (4 \times 14))$$

Step3: Calculate inner terms

$$SA = 2(68 + 238 + 56)$$

Step4: Sum and multiply by 2

$$SA = 2(362) = 724$$

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5)

Step1: Identify dimensions

$l=13\ \text{ft}, w=4\ \text{ft}, h=19\ \text{ft}$

Step2: Substitute into formula

$$SA = 2((13 \times 4) + (13 \times 19) + (4 \times 19))$$

Step3: Calculate inner terms

$$SA = 2(52 + 247 + 76)$$

Step4: Sum and multiply by 2

$$SA = 2(375) = 750$$

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6)

Step1: Identify dimensions

$l=14\ \text{in}, w=9\ \text{in}, h=3\ \text{in}$

Step2: Substitute into formula

$$SA = 2((14 \times 9) + (14 \times 3) + (9 \times 3))$$

Step3: Calculate inner terms

$$SA = 2(126 + 42 + 27)$$

Step4: Sum and multiply by 2

$$SA = 2(195) = 390$$

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7)

Step1: Identify dimensions

$l=12\ \text{ft}, w=2\ \text{ft}, h=7\ \text{ft}$

Step2: Substitute into formula

$$SA = 2((12 \times 2) + (12 \times 7) + (2 \times 7))$$

Step3: Calculate inner terms

$$SA = 2(24 + 84 + 14)$$

Step4: Sum and multiply by 2

$$SA = 2(122) = 244$$

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8)

Step1: Identify dimensions

$l=11\ \text{in}, w=6\ \text{in}, h=4\ \text{in}$

Step2: Substitute into formula

$$SA = 2((11 \times 6) + (11 \times 4) + (6 \times 4))$$

Step3: Calculate inner terms

$$SA = 2(66 + 44 + 24)$$

Step4: Sum and multiply by 2

$$SA = 2(134) = 268$$

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9)

Step1: Identify dimensions

$l=8\ \text{yd}, w=4\ \text{yd}, h=15\ \text{yd}$

Step2: Substitute into formula

$$SA = 2((8 \times 4) + (8 \times 15) + (4 \times 15))$$

Step3: Calculate inner terms

$$SA = 2(32 + 120 + 60)$$

Step4: Sum and multiply by 2

$$SA = 2(212) = 424$$

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10)

Step1: Identify dimensions

$l=18\ \text{yd}, w=8\ \text{yd}, h=12\ \text{yd}$

Step2: Substitute into formula

$$SA = 2((18 \times 8) + (18 \times 12) + (8 \times 12))$$

Step3: Calculate inner terms

$$SA = 2(144 + 216 + 96)$$

Step4: Sum and multiply by 2

$$SA = 2(456) = 912$$

Answer:

1. $366\ \text{square inches}$
2. $448\ \text{square yards}$
3. $748\ \text{square feet}$
4. $724\ \text{square yards}$
5. $750\ \text{square feet}$
6. $390\ \text{square inches}$
7. $244\ \text{square feet}$
8. $268\ \text{square inches}$
9. $424\ \text{square yards}$
10. $912\ \text{square yards}$