Question

One side of a parallelogram is 8cm if the corresponding altitude is 6cm then its area is given by
a) $ 24 $ sq cm
b) $ 36 $ sq cm
c) $ 40 $ sq cm
d) $ 48 $ sq cm

Answer 1

Hint: The question is from the concept of area of a parallelogram. A parallelogram is a geometric shape where two opposite sides are equal in length and are parallel to each other. The area of a parallelogram can be determined by various methods. In our case the base and altitude is given so we will be using the formula that deals with base and altitude to find the area of a parallelogram.
The area of a parallelogram with base $ b $ and height $ h $ is given by the formula:
 $ A = b \times h $

Complete step by step solution:
Let’s first draw the parallelogram with the given side $ 8 $ cm and the corresponding altitude $ 6 $ cm.

Here, we have side $ AB = CD = 8 $ cm and altitude $ CE = 6 $ cm.
So we have,
Base, $ b = 8 $ cm and height, $ h = 6 $ cm.
So area of parallelogram $ ABCD $ is:
$\Rightarrow A = 8 $ cm $ \times 6 $ cm $ = 48 $ sq. cm.
The area of the parallelogram is $ 48 $ sq. cm.
So, the correct answer is “Option D”.

Additional information:
The other ways to calculate the area of a parallelogram are:
1)If the length of two sides of a parallelogram is known and the angle between any two sides is known then by the application of trigonometry we have:
 $ A = ab\sin x $ , where $ a,b $ are the length of two adjacent sides and $ x $ is the angle between them.
2)If the length of two diagonals are given $ {d_1},{d_2} $ and the angle between them is $ x $ ,
 $ A = \dfrac{1}{2} \times {d_1} \times {d_2}\sin x $

Note: Notice that the unit of measurement of are is in sq. cm because the area is determined by multiplication of two quantities with the same unit of length. Omitting this unit is a common mistake, so take care of this while writing the solution.