Getting into Solids: Pyramids - ETA hand2mind

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20 cm
20 cm
10 cm
GETTING INTO SOLIDS — PRISMS
Worksheet 17: Answer Key
Surface Area
Challenge
Find the surface area of the rectangular prism with a
10 cm x 12 cm hole through the center. Describe
your process through a series of clearly shown
mathematical steps.
Step 1: I will find the surface area of the large rectangular prism and subtract the area of the two
10 cm x 12 cm regions.
First, I will find the Second, I will find the L.A. Third, I will find the area
perimeter of the base, P. L.A. = P h of the base, B.
P = 2 w + 2 l L.A. = 80(10) B = l w
P = 2(20) + 2(20) L.A. = 800 B = 20(20)
P = 80 B = 400
Fourth, I will calculate Fifth, I will find the area Finally, the surface area of
the surface area of the of the two open regions that the outside region of the large
rectangular prism using 10 cm x 12 cm. rectangular prism is the S.A. less
the S.A. formula. A = 2(lw) the area of the two open regions.
S.A. = L.A. + 2 B A = 2(10)(12) S.A. = 1,600 - 240
S.A. = 800 + 2(400) A = 240 S.A. = 1,360
S.A. = 1,600
Step 2: I will calculate the lateral area of the inside rectangular prism with 10 cm x 12 cm dimensions.
First, I will find the perimeter of Second, I will find the lateral area, L.A.
the base, P, of the 12 x 10 region. L.A. = P h
P = 2 l + 2 w L.A. = 44(10)
P = 2(12) + 2(10) L.A. = 440
P = 44
Step 3: Iʼll combine the S.A. of the outside region plus the L.A. of the inside region.
S.A. = Surface area of the outside region + inside lateral area
S.A. = 1,360 + 440
S.A. = 1,800 cm 2 1,800 cm 2
Solution: ______________________________
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