Question

The area of a trapezium is 360 cm and its height is 18 cm. If one of the parallel sides is longer than
other by 4 cm, find the lengths of parallel sides.

Please do it fast it's urgent ​

Answer 1

To Find :–

The Area of the Trapezium.

Given :–

• Area of the Trapezium = 360 cm²

• Height of the Trapezium = 18 cm

We know :–

⠀⠀⠀⠀⠀⠀Formula for

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Area of a Trapezium :

$\boxed{\bf{A = \dfrac{1}{2} \times (a + b) \times h}}$

Where :-

• A = Area of the Trapezium.

• a = Parallel side of the Trapezium.

• b = Parallel side of the Trapezium.

• h = Height of the Trapezium.

Concept :-

Let the first parallel side be x .

According to the Question , the other parallel side is 4 cm more than the first parallel side.i.e,

The other parallel side is (x + 4).

Now , by putting this value in the formula for area of a Trapezium , we can find the required value.

Solution :-

Given :-

• a = x cm

• b = (x + 4) cm

• A = 360 cm²

• h = 18 cm

By using the formula and substituting the values in it, we get :-

$:\implies \bf{A = \dfrac{1}{2} \times (a + b) \times h} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{2} \times (x + x + 4) \times 18} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{2} \times (2x + 4) \times 18} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{2} \times 2(x + 2) \times 18} \\ \\ \\ :\implies \bf{360 = \dfrac{1}{\not{2}} \times \not{2}(x + 2) \times 18} \\ \\ \\ :\implies \bf{360 = (x + 2) \times 18} \\ \\ \\ :\implies \bf{360 = 18x + 36} \\ \\ \\ :\implies \bf{360 - 36 = 18x} \\ \\ \\ :\implies \bf{324 = 18x} \\ \\ \\ :\implies \bf{\dfrac{324}{18} = x} \\ \\ \\ :\implies \bf{18 = x} \\ \\ \\ \therefore \purple{\bf{x = 18 cm}}$

Hence, the value of x is 18 cm.

⠀⠀⠀⠀⠀⠀First parallel side :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀a = x = 18 cm

⠀⠀⠀⠀⠀⠀⠀⠀→⠀b = (x + 4)

⠀⠀⠀⠀⠀⠀⠀⠀⠀=> (18 + 4) cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀=> 22 cm

Hence, the two parallel sides are 18 cm and 22 cm.