The shape of a garden is rectangular in the middle and semicircular 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) metres]
Answers
Total area of the garden = Area of the rectangular portion + The sum of the areas of the pair of semi-circles
=l.b+2×
2
1
πr
2
=(13×7)m
2
+(
2×
2
1
×
7
22
×3.5×3.5
)m
2
=(91+38.5)m
2
=129.5m
2
.
Perimeter of the garden =2× length of rectangular portion + circumference of the circle
=(
2×13+2×
7
22
×3.5
)m
=(26+22)m=48m.
thanks
To find the area and perimeter of the garden, we need to calculate the areas and perimeters of the rectangular and semicircular portions separately and then add them together.
Let's start by calculating the area of the rectangular portion:
Length of rectangle = 20 - (3.5 + 3.5) = 20 - 7 = 13 meters
Now, let's calculate the area of the semicircular portions:
Since the shape is symmetrical, we can consider only one semicircle and then double the result.
The radius of the semicircle is half the length of the rectangular portion, which is 13/2 = 6.5 meters.
The area of a semicircle is given by the formula: (π * r^2) / 2, where π is approximately 3.14 and r is the radius.
Area of one semicircle = (3.14 * 6.5^2) / 2 = 3.14 * 42.25 / 2 ≈ 66.59875 square meters
Since we have two semicircles, the total area of the semicircular portions is: 2 * 66.59875 = 133.1975 square meters
Now, we can calculate the total area of the garden by adding the area of the rectangular and semicircular portions:
Total area = Area of rectangle + Area of semicircles = 13 + 133.1975 ≈ 146.1975 square meters
To calculate the perimeter of the garden, we need to consider the perimeter of the rectangular portion and the circumference of the semicircular portions.
The perimeter of the rectangular portion is given by: 2 * (length + width)
Perimeter of rectangle = 2 * (13 + 20) = 2 * 33 = 66 meters
The circumference of a semicircle is given by: π * radius + diameter.
Circumference of one semicircle = 3.14 * 6.5 + 2 * 6.5 = 20.41 + 13 = 33.41 meters
Since we have two semicircles, the total circumference of the semicircular portions is: 2 * 33.41 = 66.82 meters
Finally, we can calculate the total perimeter of the garden by adding the perimeter of the rectangular portion and the circumference of the semicircular portions:
Total perimeter = Perimeter of rectangle + Circumference of semicircles = 66 + 66.82 = 132.82 meters
Therefore, the area of the garden is approximately 146.1975 square meters and the perimeter is approximately 132.82 meters.