A sports field has a shape that consists of semi circle and a rectangle as shown on the diagram on the right. The width of the field is 20m and its longest lengths measures 40 m. Find the area and the perimeter of the field.

You know that the diameter of the circle is 20 m, and the two ends of the field make the full circle. The perimeter of a circle is given by the equation (pi)x(diameter)

So total perimeter =
= circle + the two long sides of the field
= (3.14159265)x 20 + 40m +40m
=

The vertical distance across the semi-circle = Dia./2 = 20/2 = 10 m.,

The width of the rectangle = 20 m.,
The length of the rectangle = 40-10 = 30 m.,

A = pi*r^2/2 + L*W = (3.14*10^2/2) + 30*20 = 757 m^2.
P = Pi*Dia./2 + 2L + W = (3.14*20/2) + 2*30 + 20 = 111.4 m.

To find the area of the field, we need to find the area of both the rectangle and the semicircle, and then add them together.

1. Area of the rectangle:
The width of the field is 20m and its length (which is the same as the length of the rectangle) is 40m. The formula for the area of a rectangle is length × width.

Area of rectangle = 20m × 40m = 800 square meters

2. Area of the semicircle:
The semicircle has a radius, which is half the width of the field (10m). The formula for the area of a semicircle is 1/2 × π × radius^2.

Area of semicircle = 1/2 × π × (10m)^2 = 1/2 × π × 100m^2 = 50π square meters (or approximately 157 square meters)

3. Total area of the field:
Add the area of the rectangle and the area of the semicircle.

Total area = Area of rectangle + Area of semicircle
= 800 square meters + 50π square meters (or approximately 157 square meters)
≈ 800 + 157 square meters
≈ 957 square meters

Therefore, the area of the field is approximately 957 square meters.

To find the perimeter of the field, we need to find the perimeter of the rectangle and add the circumference of the semicircle.

1. Perimeter of the rectangle:
Since the width of the field is 20m and the length (which is same as the length of the rectangle) is 40m:

Perimeter of rectangle = 2(length + width)
= 2(40m + 20m)
= 2(60m)
= 120m

2. Circumference of the semicircle:
The semicircle has a radius of 10m. The formula for the circumference of a semicircle is π × radius + diameter.

Circumference of semicircle = π × 10m + 2 × 10m
= 10πm + 20m
= (10π + 20) meters (or approximately 62.83 meters)

3. Total perimeter of the field:
Add the perimeter of the rectangle and the circumference of the semicircle.

Total perimeter = Perimeter of rectangle + Circumference of semicircle
≈ 120m + (10π + 20)m
≈ 120m + 10πm + 20m
≈ (120 + 20)m + 10πm
≈ 140m + 10πm

Therefore, the perimeter of the field is approximately 140m + 10πm.

To find the area and perimeter of the sports field, we need to calculate the areas of the rectangle and the semicircle, and then add them together.

1. Area of the rectangle:
The width of the field is given as 20m, and the longest length as 40m. Since the rectangle is a straight-sided shape, the area can be calculated simply by multiplying the width by the length.
Area of the rectangle = width × length
Area of the rectangle = 20m × 40m
Area of the rectangle = 800 square meters

2. Area of the semicircle:
The semicircle's diameter is equal to the width of the field, which is 20m. The formula to find the area of a semicircle is:
Area of the semicircle = 1/2 × π × radius^2
First, we need to find the radius of the semicircle, which is half of the diameter.
Radius = 20m / 2
Radius = 10m

Now, we can plug the radius into the area formula:
Area of the semicircle = 1/2 × π × 10m^2
Area of the semicircle ≈ 157 square meters (rounded to the nearest whole number)

3. Total area of the field:
To get the total area of the field, we just need to add the areas of the rectangle and the semicircle.
Total area = Area of the rectangle + Area of the semicircle
Total area = 800 square meters + 157 square meters
Total area ≈ 957 square meters (rounded to the nearest whole number)

4. Perimeter of the field:
To find the perimeter, we need to consider the straight sides of the rectangle and the curved side of the semicircle.
Perimeter of the rectangle = 2 × (width + length)
Perimeter of the rectangle = 2 × (20m + 40m)
Perimeter of the rectangle = 2 × 60m
Perimeter of the rectangle = 120m

Perimeter of the semicircle = 1/2 × circumference of a full circle
The circumference of a full circle can be calculated using the formula: Circumference = 2 × π × radius.
Perimeter of the semicircle = 1/2 × 2 × π × 10m
Perimeter of the semicircle ≈ 31.4 meters (rounded to one decimal place)

Total perimeter = Perimeter of the rectangle + Perimeter of the semicircle
Total perimeter = 120m + 31.4m
Total perimeter ≈ 151.4 meters (rounded to one decimal place)

So, the area of the field is approximately 957 square meters and its perimeter is approximately 151.4 meters.