We can formulate an expression for the surface area of the attic like this:
The area of a triangle is given by the following formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the base and h is the height of the triangle.
The area of a rectangle is given by the following formula:
[tex]A=w\times l[/tex]Where w is the width and l is the length of the rectangle.
In this case, the attic has three rectangular faces, all of them have a width of 45 ft. two of them have a length of 25 ft and one has a width of 40 ft, then we can calculate the areas of these faces like this:
[tex]\begin{gathered} A1=45\times40 \\ A2=45\times25 \\ A3=45\times25 \end{gathered}[/tex]By summing up these areas, we get the area of the rectangular faces:
[tex]A=45\times40+45\times25+45\times25[/tex]From this expression, we can factor 45 to get:
[tex]A=45\times(40+25+25)[/tex]For the two triangular faces, their height equals 15 ft and the length of the bases equals 40 ft, then their areas are:
[tex]\begin{gathered} A1=\frac{15\times40}{2} \\ A2=\frac{15\times40}{2} \end{gathered}[/tex]By summing them up, we get the area of the triangular faces:
[tex]A=\frac{15\times40}{2}+\frac{15\times40}{2}=15\times40[/tex]By summing the area of the rectangular faces and the area of the triangular faces, we get the expression to calculate the total surface area of the attic, like this:
[tex]A=45(40+25+25)+40\times15=4650[/tex]Then, the net Linda draw is correct. The first term of Linda's expression 45(40+25+25) is correct. The second term of Linda's equation missing a factor of 2. The surface area of Linda's attic is 4650 square feet
