Thread: Maximum aea of rectangular field surmounted by two semicircular fields.

A rectangular field with base x and height 2r is surmounted by two semicircular fields, as shown in the diagram below. The external perimeter of the fields (solid blue track) is 200 meters. Answer the following:
a) Express the area of the rectangular field (shaded green) in terms of r
Area =

b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.)
Maximum area = (square meters)


I do not know where to even begin on this problem if anyone could help me. Any explanation as to what strategy i should use would be awesome.

First step is to draw a picture of the shapes decribed.

Then label the picture with the information for x and 2r.

Then make an expression for the perimeter with this information.

I.e. x+x+.... = 200.

Originally Posted by willjones2010

A rectangular field with base x and height 2r is surmounted by two semicircular fields, as shown in the diagram below. The external perimeter of the fields (solid blue track) is 200 meters. Answer the following:
a) Express the area of the rectangular field (shaded green) in terms of r
Area =

b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.)
Maximum area = (square meters)


I do not know where to even begin on this problem if anyone could help me. Any explanation as to what strategy i should use would be awesome.

Are you expected to use calculus?