Download
1 / 6
70 likes | 216 Views
A farmer aims to enclose a part of his large field for sheep using 320 meters of fencing. This investigation evaluates different geometric shapes, including square, rectangular, regular pentagon, hexagon, regular octagon, circular, quarter-circle, and parallelogram. By comparing areas achievable with the available fencing, we determine which shape provides the maximum area. The results reveal that the circular design offers the largest area of approximately 8148 square meters, prompting questions about other possible shapes that might optimize space further.
E N D
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?
Solution Square - 6400 Rectangle – 6400 Pentagon – 7040 Hexagon – 7380.8 Octagon – 7728 Circle - 8148.7 Quarter Circle – 6307.7 Parallelogram – 6400.
