The area of a square ABCD is 64sq.cm.Find the area of square obtained by joining the mid-points of the sides of the square ABCD.
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Area of square ABCD = 64 sq.cm
(side)sq. = 64 cm
AB = √64
AB = 8cm
In ∆ABP
P is the mid point of AB
A is the mid point of AD
By mid point theorem
PQ = 1/2 DB.................. equation 1
In ∆ADB, By pyth. theorem
AD ^ + AB^ = BD^
8^ + 8^= BD^
BD^ = 64 + 64
BD = √120
BD = 8√2
Substituting value of BD in equation 1
PQ = 1/2 × 8√2
PQ = 4√2
Area = (16 × 2) = 32cm.
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