Question

the area of a trapezium is 216 cm cube. the lengths of the parallel sides are 13cm and 23cm respectively, find the distance between them.(please mark that its 216 cm CUBE)​

Answer 1

Trapezium = ½ × ( sum of its parallel sides )

216cm = ½ × ( 13cm + 23cm )

216cm = ½ × 36cm

216cm = 18cm

216cm/18cm

12cm

Hence distance between their parallel sides is 12cm.

Answer 2

Let the distance b/w the parallel sides be x and lengths of the Parallel sides are 13cm and 23cm.

• Area of the Trapezium = 216 cm³

We know that, we can find distance b/w them using Formula as:-

$\bullet \ {\green{\pmb{\underline{\boxed{\sf{ Area_{(Trapezium)} = \dfrac{1}{2} \times (sum \ of \ parallel \ sides ) \times (Distance \ b/w \ Parallel \ sides) }}}}}}$

$\\ \colon\implies{\sf{ 216 = \dfrac{1}{2} \times (13+23) \times x }} \\ \\ \\ \colon\implies{\sf{ 216 = \dfrac{1}{ \cancel{2} } \times ( \cancel{36} ) \times x }} \\ \\ \\ \colon\implies{\sf{ 216 = 18 \times x }} \\ \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{216}{18} } = x }} \\ \\ \\ \colon\implies{\underline{\boxed{\mathfrak\pink{ x = 12 }}}}$

Hence,

$\\ {\underline{\sf{ The \ distance \ b/w \ the \ parallel \ sides \ is \ 12 \ cm. }}}$