In the figure 2 semicircles, each of diameter 28m, are removed from the rectangle. Find (i) the perimeter, (ii) the are, of the shaded region.

banganX 2021-05-21 Answered
In the figure 2 semicircles, each of diameter 28m, are removed from the rectangle. Find
(i) the perimeter,
(ii) the are,
of the shaded region.

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Expert Answer

Roosevelt Houghton
Answered 2021-05-22 Author has 17650 answers

(i)The perimeter is sum of the two lengths and the two half-circumferences, with radius \(28/2=14 cm\):
\(\displaystyle{P}={40}+{40}+{\left(\frac{{1}}{{2}}\right)}{\left[{2}π{\left({14}\right)}\right]}+{\left(\frac{{1}}{{2}}\right)}{\left[{2}π{\left({14}\right)}\right]}\)
\(\displaystyle{P}={80}+{14}π+{14}π\)
\(\displaystyle{P}={80}+{28}π\sim{167.96}{c}{m}\)
(ii)The area is the area of the rectangle minus the areas of the two semicircles: \(\displaystyle{A}={\left({40}\right)}{\left({28}\right)}-{\left(\frac{{1}}{{2}}\right)}{\left(π\cdot{14}^{{2}}\right)}-{\left(\frac{{1}}{{2}}\right)}{\left(π\cdot{14}^{{2}}\right)}\)
\(\displaystyle{A}={1120}-{98}π-{98}π\)
\(\displaystyle{A}={1120}-{196}π\sim{504.25}{c}{m}^{{2}}\)

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