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Area of a Rectangle

The plan of a...

Question

The plan of a survey plotted to a scale of 20 m to 1 cm is reduced in such a way that a line originally 20 cm long measures 18 cm. The area of the reduced plan is measured as 324 $c m^{2}$ . The actual area (in hectare) of the survey is ______
16

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Solution

The correct option is A 16
$S h r i n k a g e f a c t o r = \frac{18}{20} = 0.9$

$R e d u c e d p l a n a r e a = (S h r i n k a g e f a c t o r)^{2} \times A c t u a l p l a n a r e a$
$324 = {(0.9)}^{2} \times A c t u a l p l a n e a r e a$

$∴ A c t u a l p l a n a r e a = 400 c m^{2}$

$∴ A c t u a l a r e a o f s u r v e y (i n h a) = 400 \times \frac{{(20)}^{2}}{10^{4}}$
$= 16 h e c t a r e s$

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