Question

There are 3 semicircles in the given figure. AB = 14 cm and C is the midpoint of AB. Find the perimeter and area of the figure. [3 MARKS]

Answer 1

Concept: 1.5 Marks
Solution: 1.5 Marks

Perimeter of 2 small semicircles
$=2\pi r$ where $r=\frac{7}{2}cm$

$\Rightarrow 2\times \frac{22}{7}\times \frac{7}{2}=22cm$

Length of the arc of the large semicircle
$=\pi R$ where R=7 cm

$\Rightarrow \frac{22}{7}\times 7=22cm$

$\therefore$ Total Perimeter
$=2\pi r+\pi R=22+22=44cm$

Total area of the figure = Area of two small semicircles + Area of one large semicircle

$=\pi r^2+\frac{\pi R^2}{2}=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2+\frac{1}{2}\frac{22}{7}\times 7^2$

$=38.5+77=115.5c{m}^2$