Find the area of a square PQRS formed by joining the mid-points of sides of another square ABCD of side 9√2cm.
Open in App
Solution
Verified by Toppr
⇒AB=BC=CD=AD=9√2cm [ Given ]
⇒AP=12AB [ P is midpoint of AB ]
⇒AP=12×9√2=9√22cm
∴AP=AS=9√22
⇒∠PAS=90o [ Angle of square is 90o ]
In right angled △PAS
⇒(PS)2=(AP)2+(AS)2 [ By Pythagoras theorem ]
⇒(PS)2=(9√22)2+(9√22)2
⇒(PS)2=1624+1624
⇒(PS)2=3244
⇒(PS)2=81
∴PS=9cm
⇒ Area of square PQRS=(9)2=81cm2
Was this answer helpful?
33
Similar Questions
Q1
Find the area of a square PQRS formed by joining the mid-points of sides of another square ABCD of side 9√2cm.
View Solution
Q2
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.
View Solution
Q3
Let S1 be a square of side 5 cm. Another square S2 is drawn by joining the mid-points of the sides of S1. Square S3 is drawn by joining the mid-points of the sides of S2 and so on. Then, (area of S1+ area of S2+ area of S3+⋯+ area of S10) is
View Solution
Q4
ABCD is a square PQRS is a square formed by joining the mid-points of AB BC CD and AD respectively. EFGH is a square formed by joining the mid-points of PQ, QR, RS and PS respectively. Find the sum of the perimeters of ABCD, PQRS and EFGH if the area of square EFGH is 25cm2.
View Solution
Q5
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD taken in order is a square only, if