The shape of a garden is rectangular in the middle and semicircular at each end as shown in the figure. Find the area and perimeter of the garden.

Given:

Total length of garden = 20 m

Radius of the circle = $\dfrac{7}{2}$ m

Length of rectangle = total length - 2 x radius of the circle

= 20 - 2 x $\dfrac{7}{2}$ m

= 20 - 7 m

= 13 m

Perimeter of the figure = l + l + 2 x $\dfrac{1}{2}$ x circumference of semicircle

As we know that circumference of the circle = 2πr

= 13 + 13 + 2 x $\dfrac{1}{2}$ x 2πr

= 26 + 2 x $\dfrac{22}{7} \times \dfrac{7}{2}$

= 26 + $\cancel{2} \times \dfrac{22}{\cancel{7}} \times \dfrac{\cancel{7}}{\cancel{2}}$

= 26 + 22

= 48 m

Area of the figure = Area of rectangle + 2 x Area of semicircle

As we know that area of rectangle = length x breadth

And, area of the circle = πr²

So, area

$= 13 \times 7 + \dfrac{22}{7} \times \big( \dfrac{7}{2} \big)^2 \\[1em] = 91 + \dfrac{22}{7} \times \dfrac{49}{4} \\[1em] = 91 + \dfrac{22 \times 49}{7 \times 4} \\[1em] = 91 + \dfrac{1078}{28} \\[1em] = 91 + 38.5 \\[1em] = 129.5 \text{ m}^2$

Hence, the area of the garden is 129.5 m² and the perimeter is 48 m.