Maths-
General
Easy
Question
The lengths of two adjacent sides of a parallelogram are respectively 51cm and 37cm. If one of its diagonal is 20cm then find the area of the parallelogram.
Hint:
area of parallelogram ABCD = area of Δ ABC + area of Δ ADC
In parallelogram diagonal divide the area in to two equal parts
I.e area of Δ ABC = area of Δ ADC.
Find area of area of Δ ABC by heron's formula for finding the area of triangle
The correct answer is: 612 cm2
Ans :- 612 (in sq.centimeters)
Explanation :-
Step 1:- Find the area of Δ ABC from heron's formula
Here, side length of triangle are 51,37 and 20 cm
Heron's formula for area of triangle with side length
a,b,c are Area 
Where s = 
Let a = 51;b = 37 ;c = 20 We get s = 
= 54
Area of Δ ADC = 
= 
We get the area of Δ ABC = 306 (cm2).
Step 2:- Find the area of Δ ADC.
In parallelogram diagonal divide the area in to two equal parts
area of Δ ABC = area of Δ ADC
area of Δ ADC = 306 (cm2).
Step 3:- Find the total area of parallelogram
area of parallelogram ABCD = area of Δ ABC + area of Δ ADC
area of parallelogram ABCD = 306 (cm2)+ 306 (cm2)
∴Area of parallelogram ABCD = 612 (cm2).
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