Question

the area of trapezium is 540 m2. two of its parallel sides are 40 m and 32 m. find the distance between two parallel sides.​

Answer 1

Answer :–

• Difference between both parallel sides (h) = 15m.

Given :–

• Area of a trapezium = 540m².
• Two parallel sides = 40m and 32m.

To Find :–

• Difference between two parallel sides. It also means, that we need to find the height (h) of the Trapezium.

Solution :–

We know that,

Area of the trapezium,

↣ $\orange{\tt \dfrac{1}{2} \times Sum \: of \: the \: parallel \: sides \times Height \: (h) }$

Here the given values are,

• Sum of the parallel sides = 40m + 32m.
• Area of the trapezium = 540m².

So,

↣ $\dfrac{1}{2} \times (40 + 32)m \times h = 540 {m}^{2}$

↣ $\dfrac{1}{ \cancel2} \times \cancel{72}m \times h = 540 {m}^{2}$

↣ $1 \times 36m \times h = 540 {m}^{2}$

↣ $36m \times h = 540 {m}^{2}$

↣ $h = \dfrac{540 \cancel{{m}}^{2} }{36 \cancel{m}}$

↣ $h = \dfrac{ \cancel{540}}{ \cancel{36}} m$

Cut it by 2,

↣ $h = \dfrac{ \cancel{270}}{ \cancel{18} }m$

Again, cut it by 2.

↣ $h = \dfrac{ \cancel{135}}{ \cancel9} m$

Now, cut it by 3,

↣ $h = \dfrac{ \cancel{45}}{ \cancel9} m$

Again, cut it by 3.

We get,

↣ $h = 15m$

Hence,

The hight 'h' is 15m.

So, the difference between both the two parallel sides of the trapezium is 15m.

Answer 2

Solution :

$\underline{\bf{Given\::}}$

• The area of trapezium = 540 m²
• Two parallel sides of trapezium = 40 m & 32 m .

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of trapezium according to the question;

As we know that formula of the area of trapezium;

$\boxed{\bf{Area\:of\:trap. = \frac{1}{2} \times (sum\:of\:base)\times height}}$

A/q

$\mapsto\tt{\dfrac{1}{2} \times (40 + 32 ) \times h = 540 }\\\\\mapsto\tt{\dfrac{1}{\cancel{2}} \times \cancel{72} \times h = 540 }\\\\\mapsto\tt{36\times h=540 }\\\\\mapsto\tt{h=\cancel{540 /36}}\\\\\mapsto\tt{\red{h=15\:m}}$

Thus;

The distance between two parallel sides will be 15 m .