Question

the length of each of one pair of parallel sides of a paralellogram is 6 m if the area of parallelogram is 30m^2 , then the distance between that pair of parallel sides is _________?




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Answer 1

Answer :-

$\:\\\large{\boxed{\sf{Firstly,\;let's\;understand\;the\;concept\;used\;:-}}}$

Here the concept of Areas of Parallelogram has been used. We see that we are given the two parallel sides of the parallelogram. And we have to find the distance between them. For that we can assume one parallel side as Base and apply in the formula of Area of Parallelogram and find the height.

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★ Formula Used :-

$\:\\\large{\boxed{\sf{Area\;of\;Parallelogram\;=\;\bf{Base\:\times\:Height}}}}$

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★ Question :-

The length of each of one pair of parallel sides of a paralellogram is 6 m if the area of parallelogram is 30m^2 , then the distance between that pair of parallel sides is _________?

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★ Solution :-

Given,

» Area of Parallelogram = 30 m²

» Length of each parallel side = 6 m

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~ For the Evaluation from the figure :-

Let's understand the diagram first :-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf A}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf B}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf C}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf D}\end{picture}$

As you can see here, and in the attachment, AB and CD are the two parallel sides of length 6 m.

AC and BD are the two sides which are parallel but are distance between the earlier pair of parallel sides.

So,

• AB = CD = 6 m

• AC = BD = ?

Here we have to find the length of AC of BD. We can take them as Height of parallelogram. So both the sides are equal, so we can find any one of them.

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~ For the Length of Height of Parallelogram :-

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Areas\;of\;Parallelogram\;=\;\bf{Base_{(AB)}\:\times\:Height_{(AC)}}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Base_{(AB)}\;\times\;Height_{(AC)}\;=\;\bf{30\;m^{2}}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:6\;\times\;Height_{(AC)}\;=\;\bf{30}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Height_{(AC)}\;=\;\bf{\dfrac{30}{6}\;\:=\;\:\underline{\underline{5\;\;m}}}}}$

Here we see that we get the length of :-

=> AC = 5 m

So,

=> AC = BD = 5 m

From figure we see that AC and BD are the distance between the pairs of parallel sides given.

$\:\\\large{\underline{\underline{\rm{Thus,\;distance\;between\;that\;pair\;of\;parallel\;sides\;is\;\;\boxed{\bf{5\;\:m}}}}}}$

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★ More Formulas to Know :-

$\:\\\sf{\leadsto\;\;\;Area\;of\;Square\;=\;(Side)^{2}}$

$\:\\\sf{\leadsto\;\;\;Area\;of\;Rectangle\;=\;Length\:\times\:Breadth}$

$\:\\\sf{\leadsto\;\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\:\\\sf{\leadsto\;\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\:\times\:Base\:\times\:Height}$

$\:\\\sf{\leadsto\;\;\;Perimeter\;of\;Square\;=\;4\:\times\:Side}$

$\:\\\sf{\leadsto\;\;\;Perimeter\;of\;Rectangle\;=\;2\:\times\:(Length\:+\:Breadth)}$

$\:\\\sf{\leadsto\;\;\;Circumference\;of\;Circle\;=\;2 \pi r}$

* Note :- Kindly view this answer from web to see the highlighted diagram mentioned in the answer.

The image in the attachment is only drawn in the answer which is highlighted. So you can refer that also.

Answer 2

Given :-

The length of each of one pair of parallel sides of a paralellogram is 6 m if the area of parallelogram is 30m².

To find :-

Distance between pair of parallel sides.

Solution :-

• Length of each of one pair of parallel sides of a paralellogram = 6 m

• Area of parallelogram = 30 m²

• AB = DC = AD = BC = 6m

As we know that

→ Area of parallelogram = base × height

→ 30 = AB × h {AB as a base}

→ 30 = 6 × h

→ h = 30/6

→ h = 5 m

•°• Distance between pair of parallel sides is 5m

Properties of parallelogram

• Opposite angles of a llgm are equal.
• Opposite sides of parallelogram are equal.
• Diagonals of llgm bisect each other.

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