Question

find the ratio of the area of the parallelogram to the area of triangle whose base and height are same

Answer 1

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.

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

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.

Notes:

1. If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.

If they have same altitude, they will lie between the same parallels. Hence the area of the triangle will be equal to half that of the parallelogram.

2. If a triangle and a rectangle be on the same base and between the same parallels, the area of the triangle will be half that of the rectangle.

3. Area of a triangle = 1/2 × base × altitude.

Answer 2

Step-by-step explanation:

area of parallelogram (p) = bh

area of traingle (t) = ½bh

p:t = 1:½

= 2:1

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