Find the total perimeter of all the petals in each of the given flowers.                            [Page No. 130]

7. (A) Given, square with a side length of 14 cm.

Four petals inside the square, each formed by two quarter circles.

The centres of these quarter circles are the midpoints of the square's sides.

Each petal is formed by quarter circles whose centres are midpoints of the sides.

$$\text{Radius} = \frac{14}{2} = 7 \text{ cm}$$

Total petals = 4

Each petal consists of $2$ quarter circles = $1$ semicircle

So, total arcs = $4$ semicircles = $2$ full circles

$$Perimeter = 2 \times (2\pi r) = 4\pi r$$

$$= 4 \times \frac{22}{7} \times 7 = 88 \text{ cm}$$

Total perimeter of flower is 88 cm.

(B) 6-petal flower in a regular hexagon with side 42 cm:

Each petal has 2 arcs; each arc of a circle of radius = 42 cm.

Each arc subtends 60° at its centre (equilateral triangle in hexagon).

$$\text{Arc} = \frac{60}{360} \times 2\pi \times 42$$

$$= \frac{1}{6} \times 2 \times \frac{22}{7} \times 42$$

$$= \frac{1}{6} \times 2 \times 132$$

$$= \frac{264}{6} = 44 \text{ cm}$$

$$\text{Total arcs} = 12 \text{ arcs} \times 44 \text{ cm} = 528 \text{ cm}$$