Question

ABCD is a rectangle. E,F,G,H are the midpoint of sides AB,BC,CD and DA respectively.
If ar(EFGH)=16 cm square, find ar(ABCD)

Answer 1

Solution:

Solution - Given that:  ABCD is a rectangle, E,F,G,H are Mid Points of AB, BC, CD, DA, Ar(EFGH) = 16.

We have to find:  Ar(ABCD).

Construction: Join FH.

Proof:

In quad ABFH,

Ar(EFH) = 1/2 Ar(ABFH  -(1).

Similarly in quad, DCFH,

Ar( GFH ) = 1 /2 Ar( DCFH )  - (2).

From 1) and 2), we get:-

Ar ( EFGH ) = 1 / 2 Ar ( ABCD ) – (3).

Therefore Ar (EFGH ) = 16 cm .. (given).

From 3, Ar( ABCD ) = 2 x 16 = 32 cm.

Hence the Area of ABCD = 32cm