Question

Find the area of the flower bed (with semi-circular ends) as shown in the figure:

Answer 1

Step 1: Solve for area of the rectangle

Given,

1. Length of the rectangular portion $ABCD$ of the flower bed is $38cm$
2. Breadth of the rectangular portion $ABCD$ of the flower bed is $10cm$

$\therefore$Area of rectangle $ABCD$ $=$ length $\times$ breadth

$$\begin{gathered} =38\times 10 \\ =380c{m}^2 \end{gathered}$$

Step 2: Solve for area of semthe the i-circle

$\therefore$ Diameter of the semi-circle$=$ Breadth of the rectangle $ABCD$ = $10cm$

$\Rightarrow$Radius of the semi-circle $=$ $\frac{10}{2}=5cm$

$\therefore$Area of the semi-circle $=\frac{{\mathrm{\pi r}}^2}{2}=\frac{25\mathrm{\pi }}{2}c{m}^2$

Since there are two semi-circles in the flower bed,

$\therefore$Area of two semi-circles $=$ $2\times \frac{{\mathrm{\pi r}}^2}{2}=25\mathrm{\pi }{\mathrm{cm}}^2$.

Step 3: Solve for area of the flower bed

Area of the flower bed $=$ Area of the rectangular portion $+$ Area of the two semi-circles.

$$\begin{gathered} =(380+25\pi ) \\ =380+25\left(3.14\right) \\ =458.5c{m}^2 \end{gathered}$$

Hence, the area of the flower bed is $458.5c{m}^2$