## 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

Question

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 = 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) = 255.7 square units What statement best describes Kayla’s error? She used the wrong expression for the lateral faces of the solid. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)). She left out one of faces of the solid. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6). She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6). She included the face where the pyramid and prism are joined together. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) minus 2((5) (6)). SA = 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) = 255.7 square units

What statement best describes Kayla’s error?
She used the wrong expression for the lateral faces of the solid. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)).
She left out one of faces of the solid. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6).
She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6).
She included the face where the pyramid and prism are joined together. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) minus 2((5) (6))

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2 months 2021-10-17T16:12:08+00:00 2 Answers 0 views 0

Option B

Step-by-step explanation:

The reason is because the surface area is not including the base of the pyramid and the top of the prism.

Option b.  she left out one of the faces of the solid she should have simplified 2((5)(7))+2((6)(7))+2[1/2(5)(9.3)]+2[1/2(6)(9.2)]+(5)(6)

Step-by-step explanation:

we know that

The surface area of the composite figure is equal to the surface area of the pyramid not including the base plus the surface area of the prism not including the top

so

SA= 285.7 units squared