Question

9.1
practice
for use after lesson 9.1
find the surface area of the prism.
1.
2.
3.
4.

1. you buy a ring box as a birthday gift that is in the shape of a triangular prism. what is the least amount of wrapping paper needed to wrap the box?

Explanation:

1. Rectangular Prism (Problem 1)

Step1: Recall surface area formula

Surface area of rectangular prism: $SA = 2(lw + lh + wh)$

Step2: Substitute values ($l=2, w=7, h=8$)

$SA = 2((2 \times 7) + (2 \times 8) + (7 \times 8))$

Step3: Calculate inner terms

$SA = 2(14 + 16 + 56)$

Step4: Compute final value

$SA = 2(86) = 172$

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2. Triangular Prism (Problem 2)

Step1: Find area of 2 triangular bases

Area of 1 triangle: $\frac{1}{2} \times 7.2 \times 4.8$, so 2 triangles: $2 \times \frac{1}{2} \times 7.2 \times 4.8 = 34.56$

Step2: Find area of 3 rectangular faces

$A_{rect} = (6 \times 10) + (6 \times 10) + (7.2 \times 10) = 60 + 60 + 72 = 192$

Step3: Sum all areas

$SA = 34.56 + 192 = 226.56$

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3. Right Triangular Prism (Problem 3)

Step1: Find area of 2 triangular bases

Area of 1 triangle: $\frac{1}{2} \times 8 \times 6$, so 2 triangles: $2 \times \frac{1}{2} \times 8 \times 6 = 48$

Step2: Find area of 3 rectangular faces

$A_{rect} = (8 \times 12) + (6 \times 12) + (10 \times 12) = 96 + 72 + 120 = 288$

Step3: Sum all areas

$SA = 48 + 288 = 336$

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4. Rectangular Prism (Problem 4)

Step1: Recall surface area formula

Surface area of rectangular prism: $SA = 2(lw + lh + wh)$

Step2: Substitute values ($l=9, w=10, h=3$)

$SA = 2((9 \times 10) + (9 \times 3) + (10 \times 3))$

Step3: Calculate inner terms

$SA = 2(90 + 27 + 30)$

Step4: Compute final value

$SA = 2(147) = 294$

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5. Right Triangular Prism (Problem 5)

Step1: Find area of 2 triangular bases

Area of 1 triangle: $\frac{1}{2} \times 10 \times 10.5$, so 2 triangles: $2 \times \frac{1}{2} \times 10 \times 10.5 = 105$

Step2: Find area of 3 rectangular faces

$A_{rect} = (10 \times 8) + (10.5 \times 8) + (14.5 \times 8) = 80 + 84 + 116 = 280$

Step3: Sum all areas

$SA = 105 + 280 = 385$

Answer:

1. $\boldsymbol{172}$ square meters
2. $\boldsymbol{226.56}$ square meters
3. $\boldsymbol{336}$ square centimeters
4. $\boldsymbol{294}$ square inches
5. $\boldsymbol{385}$ square centimeters