Folding table

The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase?
The result round to one-hundredths.

Result

p =  67.32 %

Solution:

S=168 dm2 a=14 dm  S=a⋅ b  b=S/a=168/14=12 dm  r=b/2=12/2=6 dm  S1=π⋅ r2=3.1416⋅ 62≐113.0973 dm2  p=100⋅ S1S=100⋅ 113.0973168≐67.3198=67.32%S = 168 \ dm^2 \ \\ a = 14 \ dm \ \\ \ \\ S = a \cdot \ b \ \\ \ \\ b = S/a = 168/14 = 12 \ dm \ \\ \ \\ r = b/2 = 12/2 = 6 \ dm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 6^2 \doteq 113.0973 \ dm^2 \ \\ \ \\ p = 100 \cdot \ \dfrac{ S_{ 1 } }{ S } = 100 \cdot \ \dfrac{ 113.0973 }{ 168 } \doteq 67.3198 = 67.32 \%

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