Question

The shape of a garden is rectangular in the middle and semicircular at the end as shown in the diagram find the area and the perimeter of this Garden.​

Answer 1

Radius of semicircular ends = d/2 = 7/2 = 3.5 m

Length of rectangle = 20 - (3.5 + 3.5) = 13 m

Breadth of rectangle = 7 m

Area of garden = area of rectangle + area of two semicircles

                      = lb + 2 × ∏r2/2

                      = 13 × 7 + 22/7 × 3.52  

                      = 129.5 m2

Answer 2

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Total area of the garden = Area of the rectangular portion + The sum of the areas of the pair of semi-circles

$l.b + 2 \times \frac{1}{2}\pi {r}^{2}$

$= (13 \times 7) {m}^{2} +$

$(2 \times \frac{1}{2} \times \frac{22}{7} \times 3.5 \times 3.5) {m}^{2}$

$= (91 + 38.5) {m}^{2} = 129.5 {m}^{2}$

Perimeter of the garden =2× length of rectangular portion + circumference of the circle

$= (2 \times 13 + 2 \times \frac{22}{7} \times 3.5)m$

$= (26 + 22)m = 48m$