The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5) meters].
![The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5) meters].](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/3-1566799703.png)
Solution:
The garden is rectangular in the middle and semicircular at the ends. From the diagram, we can see that the area of the garden is the sum of the rectangular middle portion and two semicircles at the end.
Length of the rectangular part = Total length - radii of the two semicircles
= 20 − (3.5 + 3.5) meters = (20 − 7) meters = 13 meters
Breadth of the rectangular part = 7 meter
Area of the rectangular part = length × breadth = 13 meter × 7 meter = 91 sq. m
Diameter of the semi circle = 7 m
Radius of the semi circle = 7/2 m = 3.5 m
Area of the semi circle = 1/2 × π × r²
Thus, area of two semi circles = 2 × 1/2 × 22/7 × (3.5)² = 22/7 × 12.25 = 38.5 m²
Total area of the garden = (Area of rectangle) + (Area of two semicircle regions)
= 91 m² + 38.5 m² = 129.5 m²
Perimeter of the garden = length of rectangle + circumference of two semicircles + length of rectangle
= 13 + 2(π × 3.5) + 13 [Since circumference of a semicircle = πr]
= 26 + 7π
= 26 + 7 × 22/7 m
= 26 + 22 m
= 48 m
Thus, the area of the garden is 129.5 m², and the perimeter of the garden is 48 m.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 11
Video Solution:
The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5) meters]
Class 8 Maths NCERT Solutions Chapter 11 Exercise 11.1 Question 3
Summary:
The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. The area of the garden is 129.5 m², and the perimeter of the garden is 48 m.
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