Question

A triangle and a parallelogram are on the same base and betweeen the same parallels. The ratio of the areas of triangle and parallelogram is ​

Answer 1

The area of the triangle is equal to one-half area of the parallelogram

Step-by-step explanation:

A parallelogram and a rectangle on the same base and between the same parallels are equal in area. parallels, the area of the triangle is equal to one-half 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.

area of △ABD=  

 area of parallelogram ABCD

[∵,DE is the altitude of parallelogram ABCD]

Here,AB is the base and AE is the height of △ABD.

Answer:

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.

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.

∆ ABC and rectangle BCDE are on the same base BC and between the same parallels BC and ED.

Same Base and between Same Parallels

Therefore, ∆ ABC = 1/2 rectangle BCDE = 1/2 BC ∙ CD

= 1/2 BC ∙ AP [Since APCD is a rectangle]