Question

An open filed is in shape of a capsule where both ends are half circles find the area a perimeter of the open field if the diameter of the semicircles represents are sides of square that measures 50 meters length
With solution pls 😊

Answer 1

The area of the field is going to be the area of square + area of a circle

We have two semi-circles that if you put it together would make an entire circle

The area of a square is side * side
And the side length if 50

The area of a circle is \(\pi r^2\)

where r is the radius.
They told us the diameter is 50
The radius is half of the diameter. What would the radius be?

Can you find the area of the circle now?

Then add both areas to find the total area of the open field

Answer 2

Now to find the perimeter of the open field, you have to find the circumference of an entire circle

The circumference of two semi-circles is the same as the circumference of an entire circle

circumference of a circle = \( 2\pi r\)
where r is the radius
You found the radius in the previous part. It's half of the diameter.
Plug that in and find the circumference of the circle

Now to find the entire perimeter


The perimeter of the field would be
50 + 50 + circumference of the circle