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An Area Problem An Investigation

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**a) Square area b) Rectangular area.**

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.

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**c) Regular pentagon d) Hexagon**

e) Regular octagon f) Circular field

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**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?

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**Design Shape Maximum possible area**

Square Rectangle Pentagon Hexagon Octagon Circle Semi Circle Parallelogram Other shape ?

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Solution Square Rectangle – 6400 Pentagon – Hexagon – Octagon – Circle Quarter Circle – Parallelogram – 6400.

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