Question

A triangle and a rhombus are on the same base and between the same parallels. Then, find the ratio of the area of the triangle and the rhombus.

Answer 1

Hint: We know that, if a triangle and a parallelogram lie on the same base and between the same parallel lines, then the relation between their areas is: the area of the triangle is half of the area of the parallelogram. We are going to use the relation to find the required result.

Complete step-by-step answer:
It is given that a triangle and a rhombus are on the same base and between the same parallels.
We know that, if a triangle and a parallelogram lie on the same base and between the same parallel lines, then the relation between their area is:
The area of the triangle is half of the area of the parallelogram.
Now, a rhombus has an opposite pair of sides that are parallel and all the sides are equal. A parallelogram has two pairs opposite sides are equal and parallel. So, we can say that a rhombus is a special type of parallelogram.
So, the condition satisfies for a triangle and a rhombus also.
So, the relation between the area of a triangle and the rhombus which are on the same base and between the same parallels is
The area of the triangle is half of the area of the rhombus.
Therefore, the ratio of the area of the triangle and the rhombus \[1:2\].
Hence, if a triangle and a rhombus are on the same base and between the same parallels then, the ratio of the area of the triangle and the rhombus is \[1:2\].

Note: The statement is valid for a rectangle or a square with a triangle also. As a rectangle and a square is a special type of parallelogram.