Chapter 10 - Geometry - 10.4 Area and Circumference - Exercise Set 10.4 - Page 648: 41

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(a) To find the number of bags of fertilizers to be used, we need to divide the area of the lawn by \[4000\text{ f}{{\text{t}}^{2}}\](the area covered by each bag). To find the area of the lawn, we will first find the area of the whole rectangular portion and then will subtract the areas of house, shed and driveway from it. Compute the area of the whole rectangular portion as follows: \[\begin{align} & {{A}_{1}}=200\text{ ft}\times 500\text{ ft} \\ & =\text{100000 ft}{{.}^{2}} \end{align}\] Compute the area of the shed as follows; \[\begin{align} & {{A}_{2}}=20\text{ ft}\times 20\text{ ft} \\ & =400\text{ f}{{\text{t}}^{2}} \end{align}\] Compute the area of the house as follows: \[\begin{align} & {{A}_{3}}=60\text{ ft}\times 100\text{ ft} \\ & =\text{60}00\text{ f}{{\text{t}}^{2}} \end{align}\] Compute the area of the driveway as follows: \[\begin{align} & {{A}_{4}}=100\text{ ft}\times 20\text{ ft} \\ & =\text{20}00\text{ f}{{\text{t}}^{2}} \end{align}\] Compute the area of lawn as follows: \[\begin{align} & A={{A}_{1}}-\left( {{A}_{2}}+{{A}_{3}}+{{A}_{4}} \right) \\ & =100000-\left( 400+6000+2000 \right)\text{f}{{\text{t}}^{2}} \\ & =91600\text{ f}{{\text{t}}^{2}} \end{align}\] As each bag of fertilizer covers\[4000\text{ f}{{\text{t}}^{2}}\], the number of bags required to cover the lawn will be as follows: \[\begin{align} & \text{Number of bags}=\frac{91600\text{ f}{{\text{t}}^{2}}}{4000\text{ f}{{\text{t}}^{2}}} \\ & =\text{22}\text{.9} \\ & \approx \text{23} \end{align}\] Hence, the number of bag required to cover the area of the lawn is\[23\]. (b) To find the total cost of fertilizer, we will multiply the number of bags by the cost of each bag of fertilizer. So, the cost of fertilizer used is: \[\begin{align} & \text{Cost}=23\times \$25\\&=\$575\end{align}\] Hence, the total cost of fertilizer is\[\$575\].