Question
A field in the form of a parallelogram has sides 28 m and 15 m and one of the diagonal is 41 m. 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: 252 m2
Ans :- 252 (in sq. meters)
Explanation :-
Step 1:- Find the area of Δ ABC from heron's formula
Here, side length of triangle are 15,28 and 41 m
Heron's formula for area of triangle with side length
a, b ,c are Area =
Where s
Let a = 28 ;b = 15 ;c = 41 We get s = = 42
Area of Δ ADC=
We get the area of Δ ABC = 126 (m2).
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 = 126 (m2).
Step 3:- Find the total area of parallelogram
area of parallelogram ABCD = area of Δ ABC + area of Δ ADC
area of parallelogram ABCD = 126 (m2)+ 126 (m2)
∴Area of parallelogram ABCD = 252 (m2).
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