AnswersPre-Algebra BArea of Triangles

Surface Area of Composite Figures Answers

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1
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Kayla’s work to find the surface area of a composite solid formed when a rectangular prism and rectangular pyramid are joined at their bases is shown below. SA = square unitsWhat statement best describes Kayla’s error?

Question illustration
A
She used the wrong expression for the lateral faces of the solid. She should have simplified .
Option A
B
She left out one of faces of the solid. She should have simplified .
Option B
C
She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified .
Option C
D
She included the face where the pyramid and prism are joined together. She should have simplified .
Option D
2
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Devon studied the composite figure. He believed the surface area, in square units, could be found by simplifying the expression .What error did Devon make?

Question illustration
A
He used 26 instead of 24 as the slant height of one set of lateral faces.
B
He omitted the rectangle where the upper and lower solids join together.
C
He included the 34 by 20 base of the figure.
D
He believed the upper part of the figure was a pyramid instead of a prism.
3

What is the surface area of this composite solid?______________ square feet

Question illustration
A
242
B
319
C
363
D
517
4

What is the total surface area of the solid?

Question illustration
A
558 square centimeters
B
702 square centimeters
C
842 square centimeters
D
982 square centimeters
5

A cube and a square pyramid were joined to form the composite solid.What is the total surface area of the composite solid?

Question illustration
A
792 square inches
B
936 square inches
C
1,080 square inches
D
1,152 square inches
6

Two rectangular pyramids were joined at their bases to form the composite figure.What is the surface area of the figure?

Question illustration
A
1,020 cm2
B
1,175 cm2
C
1,325 cm2
D
2,050 cm2
7

Helen wants to find the surface area of the solid pictured on the left, so she constructs a net of the solid pictured on the right.Which statement best describes her work?

Question illustration
A
Helen’s net is incorrect because she forgot to include the shared rectangular face where the upper and lower solids are joined together.
B
Helen’s net is correct because she included the front, back, left, right, and bottom faces of the solid.
C
Helen’s net is incorrect because she treated the figure as a single rectangular pyramid instead of a composite shape.
D
Helen’s net is correct because she reorganized the solid as a triangular prism.
8

Which statement is true about the composite solid?

Question illustration
A
The solid has a total of 9 faces.
B
There are the same number of triangular faces as there are rectangular faces.
C
The solid is formed by joining a rectangular pyramid and a triangular prism at a common face.
D
If all of the triangular faces are congruent, then all of the rectangular faces must be congruent as well.
9

What is the surface area of the composite solid?

Question illustration
A
119 m2
B
146 m2
C
162 m2
D
174 m2
10

Joylin must stack 3 blocks identical to the one shown below.What strategy for stacking the blocks will produce a stack with the least surface area?

Question illustration
A
Create a stack where the 5-inch-by-6-inch faces of the blocks touch.
B
Create a stack where the 5-inch-by-8-inch faces of the blocks touch.
C
Create a stack where the 6-inch-by-8-inch faces of the blocks touch.
D
Create a stack where two different-sized faces of the blocks touch.

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