A school has a track that is made up of a rectangle with two semicircles at each end, as pictured. The perimeter of the track, P, is 395 m. The rectangular part of the track will be covered with grass. The grass comes in pieces that each have an area of 1.35 square metres. Determine the minimum number of pieces of grass required to cover the rectangular part of the track.

4502 pieces of grass

Step-by-step explanation:

The radius of the semicircle is 36 meters, so its perimeter is:

Perimeter = pi * radius = 113.097 m

The perimeter of both semicircles is 2 * 113.097 = 226.194 m

So if the total perimeter is 395, the length of the rectangle is:

395 = 226.194 + 2*length

2*length = 168.8

length = 84.4 m

The width of the rectangle is 2 times the radius of the semicircle, so:

width = 2 * 36 = 72 m

Then the area of the rectangle is:

Area = length * width = 84.4 * 72 = 6076.8 m2

To find the number of grass pieces, we divide the rectangle area by the grass piece area:

number of pieces = 6076.8 / 1.35 = 4501.33 pieces

So we will need 4502 pieces to cover the rectangular area.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents