Question

You have been hired to mow the neighbors lawn which looks like the polygon below. Compare the money you earn by charging a flat rate of $60 or a rate of $0.01 per square foot.

Answer 1

We need to caclulate the are of the lawn.

We will divide the lawn into the main big rectangle and the smaller triangle.

For the big rectangle calculating the area i easy:
AreaR = 125ft * 50 ft = 6250 square foot

For the triangle, we see that the triangle has a right angle. That makes it easy to calculate the area, as we just need to multiply both perpendicular sides with each other and taking the half of that.

Now one side is obviously given with 40ft. The length of the other side DE can be found quickly upon realizing that 125ft has to be equal DE plus the 75ft. It follows that DE has to be 50ft.

Therefore
AreaT = 1/2 * 40ft * 50 ft = 1000 square foot

Total Area = AreaR + AreaT = 7250 square foot.

If we would charge 1 cent per square foot, we would therefore receive
7250 square foot * $0.01/ square foot = $72.50

As $72.50 is bigger than $60 it follows that we should charge the price per square foot