Question

# 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.

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

2021-05-22

(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: $$\displaystyle{A}={\left({40}\right)}{\left({28}\right)}-{\left(\frac{{1}}{{2}}\right)}{\left(π\cdot{14}^{{2}}\right)}-{\left(\frac{{1}}{{2}}\right)}{\left(π\cdot{14}^{{2}}\right)}$$
$$\displaystyle{A}={1120}-{98}π-{98}π$$
$$\displaystyle{A}={1120}-{196}π\sim{504.25}{c}{m}^{{2}}$$