Question

pqrs is a rectangle whose sides are 8cm and 6cm. A,B,C andD are the mid points of PQ ,QR, RS and SP respectively .find the area of ABCD
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Answer 1

Given:

PQRS is a rectangle whose sides are 8cm and 6cm.

To find:

The area of ABCD.

Solution:

1) It is given that the A, B, C, and D are the mid-points of PQ, QR, RS, and SP respectively, The obtained quadilateral formed by the ABCD is the square.

2) The sides of the square are parallel to the diagonal of the rectangle PQRS.

And by the Mid-Point theorem:

the side of the square is 1/2 of the length of the diagonal of the rectangle.

3) The diagonal of the rectangle is given by:

• P²+B² = H²

• H² = 8²+6²

• H² = 64+36

• H² = 100

• H = √100

• H = 10

So the side of the square is 5 cm.

4) The area of the square is (side)²

• 5²

• 25

The area of ABCD is 25 cm².