Folding table

A folding kitchen table is rectangular with an area of 168 dm² and one side 14 dm long. If necessary, it can be enlarged by attaching two semicircular plates along the sides b. By what percentage does the table area increase? Round the result to the nearest hundredth.

Final Answer:

p =  67.32 %

Step-by-step explanation:

$$\begin{gathered} S=168{\text{dm}}^2 \\ a=14\text{dm} \\ S=a\cdot b \\ b=S/a=168/14=12\text{dm} \\ r=b/2=12/2=6\text{dm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973{\text{dm}}^2 \\ p=100\cdot \frac{S_1}{S}=100\cdot \frac{113.0973}{168}=67.32\% \end{gathered}$$

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