Question

kaylas work
sa = 2((5)(7)) + 2((6)(7)) + 2(\frac{1}{2}(5)(9.3)) + 2(\frac{1}{2}(6)(9.2)) = 255.7 square units
what statement best describes kaylas error?
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(\frac{1}{2}(5)(7 + 9.3)) + 2(\frac{1}{2}(6)(7 + 9.2)) + (5)(6).
she used the wrong expression for the lateral faces of the solid. she should have simplified 2(\frac{1}{2}(5)(7 + 9.3)) + 2(\frac{1}{2}(6)(7 + 9.2)).
she included the face where the pyramid and prism are joined together. she should have simplified 2((5)(7)) + 2((6)(7)) + 2(\frac{1}{2}(5)(9.3)) + 2(\frac{1}{2}(6)(9.2)) - 2
she left out one of faces of the solid. she should have simplified 2((5)(7)) + 2((6)(7)) + 2(\frac{1}{2}(5)(9.3)) + 2(\frac{1}{2}(6)(9.2)) + (

Explanation:

The surface area of a composite solid should include all outer - facing surfaces. In a composite solid made of a prism and a pyramid (assuming the base of the pyramid is joined to a face of the prism), the formula for the surface area should account for all the lateral faces of both the prism and the pyramid and the non - joined base of the prism (if it is a base that is exposed).
Kayla's formula \(SA = 2((5)(7))+2((6)(7)) + 2(\frac{1}{2}(5)(9.3))+2(\frac{1}{2}(6)(9.2))\) does not include the base of the prism (the face that is not part of the joined region). The correct formula should have an additional term for the base of the prism. If the base of the prism has dimensions \(5\times6\), then the formula should be \(2((5)(7))+2((6)(7)) + 2(\frac{1}{2}(5)(9.3))+2(\frac{1}{2}(6)(9.2))+(5)(6)\)

Answer:

She left out one of faces of the solid. She should have simplified \(2((5)(7)) + 2((6)(7))+2(\frac{1}{2}(5)(9.3))+2(\frac{1}{2}(6)(9.2))+(5)(6)\)