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Identifying Shapes and Areas of Different Regular Figures

What is the m...

Question

What is the maximum area of a four-sided plane with a perimeter of $12$ inches?

A

8

square inches

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B

10

square inches

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C

6

square inches

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D

9

square inches

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Solution

The correct option is D $9$ square inches
The area is maximum when the four-sided plane is a square.
The perimeter of a square $= 4 \times$ side $= 12$ inches
$\Rightarrow$ side $= 3$ inches
Now, area of the square $=$ side $\times$ side $= 3 \times 3 = 9$ square inches.

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