Question

The sum of parallel sides of a Trapezium is 28m and its area is154 metre², Then distance between the parallel sides of the Trapezium is​

Answer 1

Given:

Area of Trapezium = 154 m²

Sun of parallel sides = 28 m

To Find :

Distance between the parallel sides of the Trapezium

Theory :

•Trapezium

It is defined as a shape with four sides and one set of parallel sides.

Types of Trapezium

1. Scalene
2. Right
3. and isosceles

Properties :

Sum of all the four angles of the trapezium = 360°

Diagonals intersect each other . etc

Area :

$\sf\:Area=\dfrac{1}{2}[sum\:of\:parallel\:sides]\times\:Height$

Solution :

Let the distance between the parallel sides of the Trapezium be 'H'

Diagram :

$\setlength{\unitlength}{15mm}\begin{picture}(6,6)\put(0,1){\line(1,0){2.5}}\put(2.5,1){\line(-2,5){0.6}}\put(0,1){\line(2,5){0.6}}\put(0.6,2.5){\line(1,0){1.3}}\put(0.6,1){\line(0,1){1.5}}\put(1.1,2.6){\sf{}}\put(1.1,0.8){\sf{}}\put(0.7,1.7){\sf{H}}\end{picture}$

We know that

$\sf\implies\:A=\dfrac{1}{2}[sum\:of\:parallel\:sides]\times\:H$

Put the given values

$\sf\implies\:154=\dfrac{1}{2}\times(28)\times\:H$

$\sf\implies\:154=\dfrac{28}{2}\times\:H$

$\sf\implies\:154=14\times\:H$

$\sf\implies\:154=14H$

$\sf\implies\:H=\dfrac{154}{14}$

$\sf\implies\:H=11m$

Therefore, Distance between the parallel sides of the Trapezium is 11 m

Answer 2

Answer:

Given :-

• The sum of parallel sides of a trapezium is 28 cm and its area is 154 cm².

To Find :-

• Distance between parallel sides.

Solution :-

We know that,

$\underline{\mathcal{\red{Area\: of\: trapezium\: =\: \dfrac{1}{2} × Sum\: of\: parallel\: sides\: × Height}}}$

Given in the question :-

✯︎ Area of a trapezium = 154 cm²

✯︎ Sum of parallel sides = 28 cm

According to the question,

➛ 154 = $\dfrac{1}{2} \times 28 \times Height$

➛ 154 = 14 × Height

➛ $\cancel{\dfrac{154}{14}}$ = Height

➛ 11 = Height

➡ Height = 11 cm

$\therefore$ The distance between the parallel sides of the trapezium is 11 cm.