An Area Problem

An Investigation

An Area Problem.A farmer has 320m of fencing. He wishes to use this fencing to

enclose a small part of his large field for his sheep and gives some thought to the shape designs below.

a) Square area b) Rectangular area.

c) Regular pentagon d) Hexagon

e) Regular octagon f) Circular field

f) Quarter circle field g) Parallelogram shape

For each shape carry out an investigation and see if you can determine the ‘largest possible’ area in each case. Record your results in the table below.

Is there another shape which might give a bigger area with the 320m of fencing available?

Design Shape Maximum possible areaSquare

Rectangle

Pentagon

Hexagon

Octagon

Circle

Semi Circle

Parallelogram

Other shape ?

Solution

Square - 6400 Rectangle – 6400

Pentagon – 7040 Hexagon – 7380.8 Octagon – 7728 Circle - 8148.7

Quarter Circle – 6307.7

Parallelogram – 6400.