Question

A semicircle CDE is mounted on a parallelogram ABCE as shown, If AB = 24 cm, AE = 13 cm and EF = 12 cm,
find

(a) The perimeter of the figure,

(b) The area of the figure. [4 MARKS]

Answer 1

Conceptualisation: 1 Mark
Explanation : 1 Mark
Solution : 2 Marks

EC= AB (opposite sides of parallelogram) = 24 cm

Radius of semicircle CDE
$=\frac{1}{2}EC=12cm$

Perimeter of the figure = Length of arc CDE + EA + AB + BC

$=\left(\right(\frac{1}{2}\times 2\pi \times 12)+13+24+13)$

$=(12\pi +50)cm$

Area of the figure

= Area of semicircle CDE + Area of parallelogram ABCE

$=\left(\right(\frac{1}{2}\times \pi \times {12}^2)+(24\times 12\left)\right)$

$=(72\pi +288)c{m}^2$.

$=514.285c{m}^2$