Chapter SH, Problem 11.8MPS

i.

To determine

Calculate the area of given porch.

Answer to Problem 11.8MPS

Area of porch is $236f{t}^2$

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate the area of trapezoid. There are two trapezoids in a porch.

We know that, area of trapezoid is given as,

  $\frac{1}{2}\times height\times (longbase+shortbase)$

Now Area of trapezoid 1 is,

  $\begin{array}{l}Areaoftrapezoid1=\frac{1}{2}\times height\times (longbase+shortbase)\\ =\frac{1}{2}\times 8\times (16+10)\\ =\frac{208}{2}\\ Areaoftrapezoid1=104f{t}^2\end{array}$

Now Area of trapezoid 2 is,

  $\begin{array}{l}Areaoftrapezoid2=\frac{1}{2}\times height\times (longbase+shortbase)\\ =\frac{1}{2}\times 8\times (20+13)\\ =\frac{264}{2}\\ Areaoftrapezoid2=132f{t}^2\end{array}$

Hence

  $\begin{array}{l}Totalareaofporch=Areaoftrapezoid1+Areaoftrapezoid2\\ =104+132\\ =236f{t}^2\end{array}$

Conclusion:

Therefore, we are able to find the area of porch.

ii.

To determine

Calculate the cost of carpet required to cover the porch.

Answer to Problem 11.8MPS

Area of porch is $236f{t}^2$

Explanation of Solution

Given:

  

Cost of carpet per square foot= $1.25

Calculations:

Here, we have to calculate the cost of carpet required to cover the porch.

We have area of entire porch to be $236f{t}^2$

Cost of total carpet can be calculated as,

  $\begin{array}{l}Total\cos tofcarpet=Areaofporch\times \cos tofcarpetpersquarefoot\\ =236\times 1.25\\ =295\$\end{array}$

Conclusion:

Therefore, we are able to find the cost of carpet required to cover the porch.