Question

The area of trapezium is 34 sq cm and the length of one of the parallel side is 10cm and its height is 4cm. Find the length of the parallel side.

Answer 1

Hint: We are given that the area of trapezium is 34 sq cm, length of the one parallel side of the trapezium are 10m and height is 4m. Substitute the values in the formula of area of trapezium, $A = \dfrac{1}{2}\left( {a + b} \right)h$, where $a$ and $b$ are length of parallel lines and $h$ is the height of the trapezium to find the length of other parallel side.

Complete step by step solution: We are given that the area of a trapezium is 34 square cm.
A trapezium is a quadrilateral with a pair of parallel sides and a pair of non-parallel sides.
The length of the one side of the trapezium is 10cm and the length of its height is 4cm.
We know that area of the trapezium is $A = \dfrac{1}{2}\left( {a + b} \right)h$ ,where $a$ and $b$ are length of parallel lines and $h$ is the height of the trapezium.
On substituting the values, $A = 34$, $a = 10$ and \[h = 4\] in the above formula of area of the trapezium.
Hence, we have
$34 = \dfrac{1}{2}\left( {10 + b} \right)\left( 4 \right)$
Solve RHS by dividing 4 by 2
$34 = \left( {10 + b} \right)\left( 2 \right)$
Solve the brackets.
$34 = 20 + 2b$
Subtracting 20 on both sides,
$2b = 14$
Divide the equation throughout by 2
$b = 7$

Hence, the length of the other parallel side is 7cm.

Note: A trapezium has four sides, in which two are parallel and two are non-parallel sides. The distance between the parallel sides is the height of the trapezium. After the step, $34 = \left( {10 + b} \right)\left( 2 \right)$, we can also divide the equation by 2 and then solve for $b$ instead of opening brackets.