Maths-
General
Easy
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 cm2
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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