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

Hint: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.