ABCD is a rectangle and PQRS the figure formed by joining in order the middle points of the sides.prove that 1)PQRS is a rhombus 2) area of PQRS =1/2 AREA of ABCD

Asked by manvendra singh | 21st Nov, 2013, 10:03: PM

Expert Answer:

AC and BD are the diagonals of rectangle.
 
Now, PS = 1/2 (AC) = QR
 
And, PQ = 1/2 (BD) = RS
 
But, Ac = BD (diagonals of a rectangle are equal)
 
Thus, PQ = QR = RS = PS
 
Thus, PQRS is a rhombus.
 
Now, area of rhombus PQRS = 1/2 (product of diagonals)
 
Thus, area PQRS = 1/2 x (PR) x (QS)
 
But PR = AD = BC  and QS = AB = CD
 
And, area of rectangle = base x height = AD x CD
 
Thus, area of PQRS = 1/2 x (AD) x (CD) = 1/2 (area of rectangle ABCD)

Answered by Rashmi Khot | 22nd Nov, 2013, 11:09: AM

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