Question

The courtyard outside East Middle School is in the shape of a rectangle and half-circle.

What is the approximate area of the courtyard?

Answer 1

The correct option is the third one counting from the top. (5892 m^2)

Explanation:

First, we need to remember that:

For a rectangle of length L and width W, the area is:

A = L*W

For a circle of diameter D, the area is:

A = pi*(D/2)^2

Where pi = 3.14

In the image, we can see a rectangle and half a circle, the total area of the image will be equal to the area of the rectangle plus the area of the half circle.

In the image, we can see a rectangle of length L = 100m and width W = 50m

Then the area of the rectangle is:

A = 100m*50m = 5000m^2

And we can see that for the half-circle the diameter is D = 50m

Note that the area of a half-circle is half of the area of a complete circle, then the area of that half-circle is:

A = (1/2)*(3.14*(50m/2)^2) = 981.25 m^2

If we add these two areas we get:

Total area = 5000m^2 + 981.25 m^2 = 5981.25 m^2

If we round it up, we get:

Total area = 5982 m^2

The correct option is the third one counting from the top.