Question

1. a base of a right prism whose height is 10 feet is shown. find the surface area of the prism.
2. a base of a right prism whose height is 10 inches is shown. find the surface area of the prism.
3. a base of a right prism whose height is 10 miles is shown. find the surface area of the prism.
4. a base of a right prism whose height is 10 kilometers is shown. find the surface area of the prism.
5. a base of a right prism whose height is 10 yards is shown. find the surface area of the prism.

Explanation:

Step1: Find base - area for problem 1

Decompose the base into rectangles. The base can be seen as a large rectangle with a smaller rectangle cut - out. Area of the large rectangle with length 17 and width 7 is $17\times7 = 119$. Area of the cut - out rectangle with length $17 - 8=9$ and width $7 - 3 = 4$ is $9\times4=36$. So base area $A_{b1}=119 - 36=83$.

Step2: Find lateral - area for problem 1

The perimeter of the base $P_1$: Add up the side - lengths of the base. $P_1=7 + 17+3+(17 - 8)+4+(7 - 3)=44$. Lateral area $A_{l1}=P_1\times h=44\times10 = 440$.

Step3: Find surface - area for problem 1

Surface area $S_1 = 2A_{b1}+A_{l1}=2\times83 + 440=166+440 = 606$ square feet.

Step4: Find base - area for problem 2

Area of the large rectangle with length 12 and width 7 is $12\times7 = 84$. Area of the cut - out rectangle with length $12 - 5 = 7$ and width $7 - 2=5$ is $7\times5 = 35$. So base area $A_{b2}=84 - 35 = 49$.

Step5: Find lateral - area for problem 2

The perimeter of the base $P_2$: $P_2=7 + 12+2+(12 - 5)+5+(7 - 2)=38$. Lateral area $A_{l2}=P_2\times h=38\times10=380$.

Step6: Find surface - area for problem 2

Surface area $S_2=2A_{b2}+A_{l2}=2\times49+380 = 98 + 380=478$ square inches.

Step7: Find base - area for problem 3

Area of the large rectangle with length 12 and width 6 is $12\times6=72$. Area of the cut - out rectangle with length $12 - 4 = 8$ and width $6 - 2 = 4$ is $8\times4 = 32$. So base area $A_{b3}=72-32 = 40$.

Step8: Find lateral - area for problem 3

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Answer:

Step1: Find base - area for problem 1

Decompose the base into rectangles. The base can be seen as a large rectangle with a smaller rectangle cut - out. Area of the large rectangle with length 17 and width 7 is $17\times7 = 119$. Area of the cut - out rectangle with length $17 - 8=9$ and width $7 - 3 = 4$ is $9\times4=36$. So base area $A_{b1}=119 - 36=83$.

Step2: Find lateral - area for problem 1

The perimeter of the base $P_1$: Add up the side - lengths of the base. $P_1=7 + 17+3+(17 - 8)+4+(7 - 3)=44$. Lateral area $A_{l1}=P_1\times h=44\times10 = 440$.

Step3: Find surface - area for problem 1

Surface area $S_1 = 2A_{b1}+A_{l1}=2\times83 + 440=166+440 = 606$ square feet.

Step4: Find base - area for problem 2

Area of the large rectangle with length 12 and width 7 is $12\times7 = 84$. Area of the cut - out rectangle with length $12 - 5 = 7$ and width $7 - 2=5$ is $7\times5 = 35$. So base area $A_{b2}=84 - 35 = 49$.

Step5: Find lateral - area for problem 2

The perimeter of the base $P_2$: $P_2=7 + 12+2+(12 - 5)+5+(7 - 2)=38$. Lateral area $A_{l2}=P_2\times h=38\times10=380$.

Step6: Find surface - area for problem 2

Surface area $S_2=2A_{b2}+A_{l2}=2\times49+380 = 98 + 380=478$ square inches.

Step7: Find base - area for problem 3

Area of the large rectangle with length 12 and width 6 is $12\times6=72$. Area of the cut - out rectangle with length $12 - 4 = 8$ and width $6 - 2 = 4$ is $8\times4 = 32$. So base area $A_{b3}=72-32 = 40$.

Step8: Find lateral - area for problem 3

The[SSE Completed, Client Connection Error][LLM SSE On Failure]