Question

linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter. she needs to find the approximate surface area of the attic, including the walls, floor, and ceiling. the attic is in the shape of a triangular prism. linda draws the net and writes the expression below to represent the surface area of the attic. are lindas net and expression correct? expression for surface area of attic: 45(40 + 25 + 25)+\frac{1}{2}(40×15) click the arrows to choose an answer from each menu to explain your reasoning. the net linda drew is choose... . the first term of lindas expression, 45(40 + 25 + 25). choose... . the second term of lindas expression, \frac{1}{2}(40×15). is choose... . the surface area of lindas attic is 4,350 square feet.

Explanation:

Step1: Analyze the net

The net Linda drew is correct as it represents the 2 triangular faces and 3 rectangular faces of the triangular - prism - shaped attic.

Step2: Analyze the first term of the expression

The first term $45(40 + 25+25)$ represents the sum of the areas of the three rectangular faces. The length of the common side of the rectangles is 45 ft, and the sum of the other sides of the rectangles is $(40 + 25+25)$ ft. This part is correct.

Step3: Analyze the second term of the expression

The second term $\frac{1}{2}(40\times15)$ only accounts for one triangular face. Since a triangular prism has 2 triangular faces, this part is incorrect. It should be $2\times\frac{1}{2}(40\times15)=40\times15$.

Step4: Calculate the correct surface area

The correct surface area $S = 45(40 + 25+25)+40\times15$.
First, calculate $45(40 + 25+25)=45\times90 = 4050$.
Second, calculate $40\times15 = 600$.
Then $S=4050 + 600=4650$ square - feet.

Answer:

The net Linda drew is correct. The first term of Linda's expression, $45(40 + 25 + 25)$, is correct. The second term of Linda's expression, $\frac{1}{2}(40\times15)$, is incorrect. The surface area of Linda's attic is 4650 square feet.