A parallelogram and a triangle are on equal base and between the same parallel lines. The ratio of their areas is ______.

2:1

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3:1

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2:3

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1:2

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Solution

The correct option is A 2:1
Consider the figure given below.

In this figure, ABCD is a parallelogram and ABE is a triangle. Both of them have the same base i.e., AB. The perpendicular EF is an altitude for both triangle and parallelogram.
Now area of $Δ A B E = \frac{1}{2} A B \times E F$
And area of parallelogram is $A B \times E F$ .
Hence, Area of parallelogram is twice that of triangle and the ratio will be 2:1

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