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Q.

If The area of square ABCD is 16c m 2   then the area of the square joining the midpoint of the sides in the given figure.


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a

8c m 2  

b

3c m 2  

c

5c m 2  

d

9c m 2   

answer is A.

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Detailed Solution

Given that area of square ABCD is  16c m 2  .
Thus taking its square root we will get the length of the side of that square.
Length of side of square ABCD =  16 =4cm  
Now PQRS are the midpoint of sides AB, BC, CD and AD respectively.
So AP = PB = BQ = QC = CR = RD = DS = SA = 2cm. Is it?
seoNow look at the ∆ASP. Angle A is a right angle, also we have two sides of the triangle given. So we can use the Pythagorean theorem to find the length of the third side and that is the side of square PQRS.
Using the Pythagoras theorem for the ∆ASP.
S P 2 =A P 2 +A S 2  
Taking the square root,
⇒SP= AP+AS ⇒SP= 2 2 + 2 2 ⇒SP= 8 ⇒SP=2 2  
seoThis is the side of the inner square PQRS. So the area of the square will be,
Area = side × side
Putting the value of side,
⇒2 2 ×2 2 ⇒8c m 2  
 
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