Question

# If E, F, G and H are respectively the mid points of the sides of a parallelogram ABCD and ar(EFGH) = 40 sq.cm , find the ar (parallelogram ABCD).

Hint:

### Given , ABCD is a parallelogram with area 18 sq.cm

E,F,G and H are midpoints of parallelogram ABCD.

Now join HF and draw GI and EJ perpendicular to HF .

Draw height DJ perpendicular to base AB .

Now find the areas of triangle GHF and triangle EHF and add it to get the area of

EFGH in terms of area of parallelogram ABCD

## The correct answer is: 80cm2

### Ans :- 80 cm^{2}

Explanation :-

Step 1:- Find area of parallelogram ABCD

Let height Dk = h and base AB = b

We get area of parallelogram ABCD = base × height = bh

Step 2:- Find height GI and EJ

In parallelogram line joining midpoints of opposites sides is parallel to the base and

equal to the base length i.e HF = AB = b

Let us consider ,

Here HF // AB and passing through mid point of side AD of

So, the line intersects the side DK at midpoint L i.e DL = LK = DK/2 = h/2.

As the are the perpendicular to HF so , the are the perpendicular length between lines DC , HF and AB

As we know perpendicular length between DC and HF is h/2 then GI = h/2

As we know perpendicular length between AB and HF is h/2 then EJ = h/2

Step 3:- Find the areas of EFH and HGF

As the area of triangle = ½ base × height

Area of = ½ base length of hf × height EJ =

Area of = ½ base length of hf × height GI =

Area of EFGH = Area of + Area of =

Step 4:- Equate the areas of EFGH

We Know that area of parallelogram ABCD = bh = 80 sq.cm.

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