Question

If a wire is bent in the shape of a square, the area of the square is 81 cm. When
the same wire is bent into the form of a semicircular are bounded by its diameter,
find the area of the shape so formed. (take it
2).​

Answer 1

Answer:

ANSWER

Let the side of the square be a cm

Thus, perimeter is 4a and area of the square is a2

∴a2=81

⇒a=81

⇒a=9

Thus, perimeter =4×9 =36 cm

Now, wire is bent into a semicircle.

Therefore, 2r+πr=36

⇒r(π+2)=36 $$

⇒r=722+236

⇒r=73636

⇒r=7 cm

Area of semicircle =21πr2

=21×722×7×7

=77 cm2

Answer 2

$\huge\underbrace\mathrm\purple{Answer}$

Let the side of the square be a cm

Thus, perimeter is 4a and area of the square is a2

∴a2=81

⇒a=81

⇒a=9

Thus, perimeter =4×9 =36 cm

Now, wire is bent into a semicircle.

Therefore, 2r+πr=36

⇒r(π+2)=36 $$

⇒r=722+236

⇒r=73636

⇒r=7 cm

Area of semicircle =21πr2

=21×722×7×7

=77 cm2

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