Question

The height in the area of a parallelogram is:
(a) $\dfrac{area}{base}$
(b) $\dfrac{base}{area}$
(c) $area\times base$
(d) $area\times height$

Answer 1

Hint: In the above problem, we are asked to find the relation between height, area and base of the parallelogram so basically, we need a relation between area, base and height of the parallelogram and rearranging this relation will give us the height of the parallelogram. We know that area of a parallelogram is equal to the product of base and height and the mathematical expression of this relation will look like: $area=base\times height$ . Now, rearranging this relation will give us the height of the parallelogram.

Complete step by step solution:
We know the relation between area, base and height of the parallelogram which says that the area of the parallelogram is equal to the multiplication of base and height of that parallelogram. The mathematical expression for this multiplication is shown below:
$area=base\times height$ …………… (1)
You can understand this formula from the below picture:

In the above figure, you can see that the base of the parallelogram ABCD is BC and the height is the perpendicular dropped from the vertex A on the base BC which is equal to AE.
Now, in the above problem, we are asked to find the height of the parallelogram which we are going to deduce from eq. (1) and we get,
$area=base\times height$
Now, to find the expression for height, we are going to write “height” on one side of the above equation which we are going to do by dividing “base” on both the sides of the above equation and we get,
$\dfrac{area}{base}=height$

So, the correct answer is “Option A”.

Note: In the above problem, we are asked to find the expression for height of the parallelogram. Similarly, you can find the expression for “base and area” of the parallelogram also.
Area of the parallelogram we have already shown above in eq. (1) and base of the parallelogram is calculated by rearranging the eq. (1) in the following way:
$area=base\times height$
Dividing “height” on both the sides of the above equation we get,
$\dfrac{area}{height}=base$