Question

Two semicircular flower beds are made on the outside of the smaller sides of a rectangular garden 16 m by 7 rn. Find the total area and perimeter of the garden.

Answer 1

Given:

• Rectangle dimensions: length = 16 m, width = 7 m
• Two semicircular flower beds on the outside of the smaller sides 7 m sides
• Radius of each semicircle = `7/2` = 3.5 m
• π value used = 3.14 approximately

Step wise calculation:

1. Area of rectangle = Length × Width 

= 16 × 7

= 112 m²

2. Area of one semicircle = `1/2 xx π × r^2`

= 0.5 × 3.14 × (3.5)²

= 19.245 m²   ...(More precise calculation)

3. Area of two semicircles = 2 × 19.245 = 38.49 m²

4. Total area = Rectangle area + Area of two semicircles

= 112 + 38.49

= 150.49 m² ≈ 150.5 m²   ...(Rounded)

5. For perimeter long sides contribute: 2 × 16 = 32 m

6. Semicircular arcs together form a full circle’s circumference = 2 × π × r

= 2 × 3.14 × 3.5

= 21.98 m

7. Total perimeter = 32 + 21.98

= 53.98 m ≈ 54 m   ...(Rounded)

• Total area = 150.5 m²   ...(Rounded from 150.49)
• Total perimeter = 54 m   ...(Rounded from 53.98)

So the difference is due to more precise use of π and rounding. The rounds the area to 150.5 m² and the perimeter to 54 m for simplicity.