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, andceiling. The attic is in the shape of a triangular prism. Linda draws the net and writesthe expression below to represent the surface area of the attic. Are Linda's net andexpression correct?15 ft45 ft25 ft40 ft25 ft25 ft25 ft- 15 ft45 ft40 ft15 ftExpression for Surface Area of Attic:45 (40 + 25 + 25) + ] (40 x 15)

Answer 1

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:

`A=(b* h)/(2)`

Where b is the base and h is the height of the triangle.

The area of a rectangle is given by the following formula:

`A=w* l`

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:

`\begin{gathered} A1=45*40 \\ A2=45*25 \\ A3=45*25 \end{gathered}`

By summing up these areas, we get the area of the rectangular faces:

`A=45*40+45*25+45*25`

From this expression, we can factor 45 to get:

`A=45*(40+25+25)`

For the two triangular faces, their height equals 15 ft and the length of the bases equals 40 ft, then their areas are:

`\begin{gathered} A1=(15*40)/(2) \\ A2=(15*40)/(2) \end{gathered}`

By summing them up, we get the area of the triangular faces:

`A=(15*40)/(2)+(15*40)/(2)=15*40`

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:

`A=45(40+25+25)+40*15=4650`

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