Prove that the area of parallelogram and trapezium with same base and same parallel lines are equal
Answers
Answer:
Triangle and parallelogram on same base and between same parallels.
If a triangle and a parallelogram are on the same base and between the same parallels, then the area of triangle is equal to half the area of the parallelogram.
Step-by-step explanation:
In the adjoining figure, parallelogram ABCD and ∆ABD are on the same base AB and between the same parallels AF and DC.
Triangle and Parallelogram on Same Base and between Same Parallels
d c
____________
/|\. | /|
/. | \. | /. |
/. | \. | /. |
/. | \. | /. |
/. | \|/. |
_________________
a. e. b f
Therefore, area of ∆ABD = 1/2 area of parallelogram ABCD
= 1/2 (AB × AE)
[Since, DE is the altitude of parallelogram ABCD]
Here, AB is the base and AE is the height of ∆ABD.