Question

find the distance between the parallel side of a trapezium parallel side are 49 cm and 23cm and the area of trapezium is 864cm2​

Answer 1

GIVEN :-

• Parallel sides of trapezium = 49 and 23 cm.
• Area of trapezium = 864 cm².

TO FIND :-

• distance between the parallel sides (Height).

SOLUTION :-

$\\ : \implies \displaystyle \sf \: Area_{( Trapezium)} = \frac{1}{2} \bigg \lgroup \: sum \: of \: \parallel \: sides \bigg \rgroup \times height$

$: \implies \displaystyle \sf \:864 = \dfrac{1}{2} \bigg \lgroup 49 + 23\bigg \rgroup \times height$

$: \implies \displaystyle \sf \:864 = \dfrac{1}{2} \times 72 \times height$

$: \implies \displaystyle \sf \:864 = 36 \times height$

$: \implies \displaystyle \sf \:height = \dfrac{864}{36}$

$: \implies \underline{ \boxed{\displaystyle \sf \:height = 24 \: cm.}}$

$\therefore \underline{\displaystyle \sf \: distance \ between \ the \ parallel \ sides \ (Height) \ is \ 24 \ cm.}$

Answer 2

Given:

$\rm \bull Length \: of \: the \: parallel \: sides = 49cm \: and \: 23cm$

$\rm \bull Area \: of \: trapezium = {864cm}^{2}$

Find:

$\rm \bull Distance \: between \: parallel \: sides$

Solution:

we, know that

$\underline{\boxed{ \rm Area \: of \: trapezium = \frac{1}{2} \times (sum \: of \: parallel \: sides)(distance \: between \: them)}}$

So,

$\rm \to Area \: of \: trapezium = \frac{h}{2} \times (a + b)$

where, a and b are the parallel sides of the trapezium and h is the height.

Now,

$\rm \implies 864 = \frac{h}{2} \times (49 + 23)$

$\rm \implies 864 = \frac{h}{2} \times (72)$

$\rm \implies 864 = 36h$

$\rm \implies h = \frac{864}{36}$

$\rm \implies h = 24cm$

$\underline{ \underline{\rm \to h = 24cm}}$

_______________

Hence, the distance between the parallel sides of the given trapezium will be 24cm