Getting into Solids: Pyramids - ETA hand2mind

Name __________________________________________
2 ft
GETTING INTO SOLIDS — PRISMS
Worksheet 13: Answer Key
Surface Area
Challenge
6 ft
14 ft Find the surface area of the right solid. Describe
your process through a series of clearly shown
mathematical steps.
9 ft
10 ft
Step 1: I will find the surface area of the large rectangular prism less the surface area of the 2 x 9 area.
First, I will find the perimeter Second, I will find the Third, I will find the
of the base, P, using the formula lateral area, L.A. area of the base, B,
P = 2 l + 2 w L.A. = P h using the formula
P = 2 (10) + 2 (9) L.A. = 38 (6) B = l w
P = 20 + 18 L.A. = 228 B = 10 (9)
P = 38 B = 90
Fourth, total surface area of Finally, I will subtract 18
the large rectangular prism is (the area of the 2 x 9 area)
S.A. = L.A. + 2 B
because it is hidden by the
S.A. = 228 + 2 (90)
top rectangular prism.
S.A. = 228 + 180 S.A. = 408 - 18
S.A. = 408 S.A. = 390
Step 2: I will find the surface area of the small rectangular prism less the surface area of the 2 x 9 area.
I will find the perimeter of the Second, I will find the Third, I will find the
base, P, using the formula lateral area, L.A. area of the base, B,
P = 2 l + 2 w L.A. = P h using the formula
P = 2 (2) + 2 (9) L.A. = 22 (8) B = l w
P = 4 + 18 L.A. = 176 B = 2 (9)
P = 22 B = 18
Fourth, total surface area of Finally, I will subtract 18 (the area of the 2 x 9 area)
the small rectangular prism is because it is hidden by the bottom rectangular prism.
S.A. = L.A. + 2 B S.A. = 212 - 18
S.A. = 176 + 2 (18) S.A. = 194
S.A. = 176 + 36
S.A. = 212
Step 3: The surface area of large rectangular prism + surface area of small rectangular prism will
equal the total surface area.
S.A. = 390 + 194
S.A. = 584 ft 2
Solution: ______________________________
584 ft 2
23