Question

A bed of roses is like the adjoining diagram (figure). In the centre is a square and on each side there is semi-circle. Side of the square is 21 m. If each rose-plant needs 6 m² of space, find out the number of plants which can be planted in the whole figure.

Answer 1

Given:

Side of square = 21 m

On each side of the square, there is a semicircle

Each rose plant needs 6 m²

Step 1: Radius of each semicircle

Since the semicircle is drawn on each side of the square:

Diameter = 21 m

Radius = `21/2` = 10.5 m

Step 2: Area of the square

Area = 21²

= 441 m²

Step 3: Area of four semicircles

Area of one semicircle:

`1/2 πr^2 = 1/2 xx 22/7 xx (10.5)^2`

= `1/2 xx 22/7 xx 110.25`

= `1/2 xx 346.5`

= 173.25 m²

Area of four semicircles:

4 × 173.25 = 693 m²

Step 4: Total area of the figure

Total area = 441 + 693

= 1134 m²

Step 5: Number of rose plants

Each plant needs 6 m²:

`1134/6 = 189`