Question

The mean length of the bases of a trapezium is 150 cm. Find the area of the trapezium if its altitude is 80 cm.

Answer 1

Hint: Here, we will use the formula for area of a trapezium which is given as $Area=\dfrac{1}{2}\times \left( \text{sum of parallel sides } \right)\times height$. Here, height is the distance between the parallel sides. Also, we will use the concept of mean of two numbers. The mean of two numbers is given as the sum of two numbers divided by 2. The mean of two numbers a and b is given as $\dfrac{\left( a+b \right)}{2}$.

Complete step-by-step answer:

Since, we are given that the mean of the lengths of the parallel sides of the trapezium is 150 cm.
Let the length of the two parallel sides be x and y and the distance between them be h.
Since, the mean of x and y is given to be 150 cm, so we have:
$\dfrac{\left( x+y \right)}{2}=150cm$
Also, it is given that the altitude of the trapezium measures 80 cm.
So, h = 80 cm.
Since, the formula for the area of a trapezium is given as:
$Area=\dfrac{1}{2}\times \left( \text{sum of parallel sides } \right)\times height$
Or, $Area=\dfrac{1}{2}\times \left( x+y \right)\times h$
On putting the values of $\dfrac{\left( x+y \right)}{2}$ and h in the above equation, we get:
$A=\left( 150\times 80 \right)c{{m}^{2}}=12000c{{m}^{2}}$
Hence, the area of the trapezium is $12000c{{m}^{2}}$.

Note: Students should note here that it is not necessary to find the values of x and y as we can directly put the value of $\dfrac{x+y}{2}$ in the formula for the area of the trapezium. This will make the calculation easy.