Question

Find the base of the parallelogram if its area is $80c{m^2}$ and altitude is 10cm.
A. 6 cm
B. 8 cm
C. 10 cm
D. None of the above

Answer 1

Parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and also opposite angles of a parallelogram are equal. Area of a parallelogram is given by the formula $A = b \times h$ , where $b$ is the base of the parallelogram and $h$ is the height or the altitude of the parallelogram. In this question the area a parallelogram and the altitude length is given and we are asked to find the base of the parallelogram, so as we know the area of a parallelogram is given as $A = b \times h$ , so by substituting the values we will find the base length.

Complete step by step solution:
Given
The altitude of the parallelogram $h = 10cm$
Also the area of the parallelogram is $A = 80c{m^2}$
We are asked to find the base of the parallelogram and as we know the area of the parallelogram is $A = b \times h$ , hence by substituting the given values in the formula, we can write

$$A = b \times h \\\ 80 = b \times 10 \\\$$

Hence by further solving this equation we get

$$b = \dfrac{{80}}{{10}} \\\ = 8cm \\\$$

Therefore we can say the base of the parallelogram is $8cm$

Option B is correct.

Note: A parallelogram with base b and height h has the same area as the rectangle with base b and height h only difference between the parallelogram and the rectangle is the angle between the sides, if we make the angle between each side of given parallelogram as ${90^ \circ }$ then we will have a rectangle.