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)+1/2(40×15)

Explanation:

Step1: Analyze the net of triangular - prism

The net of a triangular prism should have two triangular faces and three rectangular faces. The net Linda drew seems to be correct as it has the appropriate number and shape of faces for a triangular - prism.

Step2: Analyze the surface - area formula

The surface area of a triangular prism \(SA=2\times(\text{area of base})+\text{sum of areas of rectangular faces}\). The area of the rectangular faces: The lengths of the rectangles are \(45\) ft and the widths are \(40\), \(25\), \(25\) ft. The sum of the areas of the rectangular faces is \(45\times(40 + 25+25)\). The area of the triangular base with base \(b = 40\) ft and height \(h = 15\) ft is \(A=\frac{1}{2}\times40\times15\), and since there are two triangular bases, the term for the bases is \(2\times\frac{1}{2}\times40\times15=40\times15\). But Linda's expression \(45(40 + 25+25)+\frac{1}{2}(40\times15)\) is incorrect because she only accounted for one triangular base.
The correct surface - area formula for this triangular prism is \(45(40 + 25+25)+40\times15\).

Answer:

The net Linda drew is correct. The first term of Linda's expression \(45(40 + 25+25)\) is correct for the sum of the areas of the rectangular faces. The second term of Linda's expression \(\frac{1}{2}(40\times15)\) is incorrect as it only accounts for one triangular base instead of two. The surface area of Linda's attic should be \(45(40 + 25+25)+40\times15\) square feet.