Question

The area of a trapezium is 180 sq.cm and its height is 9 cm.If one of the parallel sides is longer than the other by 6 cm, find the length of the parallel sides.​

Answer 1

Given :-

Area of the trapezium = 180 cm²

Height of the trapezium = 9 cm

One side is longer than the other by = 6 cm

To Find :-

The length of the parallel sides.​

Solution :-

We know that,

• h = Height
• l = Length
• b = Breadth

Given that,

Height = 180 cm²

Height = 9 cm

One side is longer than the other by = 6 cm

Let us consider the length of other parallel side to be x

Then, the length of other side will be (x + 6) cm

Area of trapezium = ½ × Sum of parallel sides × Distance between the parallel sides

Area of trapezium = $\sf \dfrac{1}{2} \times 9 \times (x+x+6)$

Substituting their values,

$\implies \sf 180=\dfrac{1}{2} \times 9 \times (x+x+6)$

$\implies \sf 360=18x+54$

Finding the value of x,

$\implies \sf 18x=360-54$

$\implies \sf 18x=306$

$\implies \sf x=\dfrac{306}{18}$

$\implies \sf x=17$

Hence, the value of x is 17

We know that, the length of other side is x + 6

By substituting 17 in x,

$\implies \sf 17+x=23$

Therefore, the two parallel sides are 17 cm and 13 cm

To Note :-

The formula to calculate the area of trapezium is:

Area = ½ × Sum of parallel sides × Distance between the parallel sides

Properties of a trapezium includes:

• A trapezium has 4 unequal sides: two parallel and two non-parallel sides.
• Sum of all interior angles is 360 degrees.
• Diagonals bisect each other.