Grass seed

Pearl wants to buy grass seed to cover her whole lawn with dimensions 7 x 11 meters, except for the pool. The pool is 5 3/4 m by 3 1/2 m. Find the area the grass seed needs to cover.

Final Answer:

A =  56 ⁷⁄₈ = 455/8 m²

Step-by-step explanation:

$$\begin{gathered} x=7\text{m} \\ y=11\text{m} \\ {S}_1=x\cdot y=7\cdot 11=77{\text{m}}^2 \\ a=5\frac{3}{4}=5+\frac{3}{4}=\frac{5\cdot 4+3}{4}=\frac{20+3}{4}=\frac{23}{4}=5.75\text{m} \\ b=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3.5\text{m} \\ {S}_2=a\cdot b=\frac{23}{4}\cdot \frac{7}{2}=\frac{23\cdot 7}{4\cdot 2}=\frac{161}{8}=20.125{\text{m}}^2 \\ A=S_1-S_2=77-\frac{161}{8}=\frac{77\cdot 8}{8}-\frac{161}{8}=\frac{616}{8}-\frac{161}{8}=\frac{616-161}{8}=\frac{455}{8}=\frac{455}{8}{\text{m}}^2=56\frac{7}{8}{\text{m}}^2=56.875{\text{m}}^2 \end{gathered}$$

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