| A piece of wire 132 cm long is bent successively in the shape of an equilateral triangle, a square, a circle and a regular hexagon. The largest area is included when the wire is bent into the shape of a [FCI (Assistant) Grade III 2015] |
A) circle
B) hexagon
C) square
D) triangle
Correct Answer: A
Solution :
| Area of equilateral triangle \[=\frac{\sqrt{3}}{4}\times {{\left( \frac{132}{3} \right)}^{2}}\] |
| \[=\frac{\sqrt{3}}{4}\times {{(44)}^{2}}=484\sqrt{3}\,c{{m}^{2}}\] |
| Area of square \[={{\left( \frac{132}{4} \right)}^{2}}=1089\,c{{m}^{2}}\] |
| Area of circle \[=\frac{22}{7}\times 441=1386\,c{{m}^{2}}\] |
| Area of regular hexagon \[=\frac{\sqrt{3}}{4}\times 6\times {{\left( \frac{132}{6} \right)}^{2}}\] |
| \[=\frac{\sqrt{3}}{4}\times 6\times {{(22)}^{2}}=\frac{\sqrt{3}}{4}\times 6\times 484\] |
| \[=\frac{2904\sqrt{3}}{4}=726\sqrt{3}\,c{{m}^{2}}\] |
| Hence, circle contains the largest area. |
You need to login to perform this action.
You will be redirected in
3 sec
