Question

Area of trapezium is 140cm2 . if length of one parallel side is 25 cm and the distance
between them is 7cm . then find the length of other side.

Answer 1

Question :

Area of trapezium is 140cm². if length of one parallel side is 25 cm and the distance between them is 7cm . then find the length of other side.

Answer :

$\bf\pink{Given:}$

• Area of Trapezium is 140 cm² .

• Length of one of the parallel side is 25 cm .

• distance between the two parallel sides or the height of the Trapezium is 7 cm .

$\bf\pink{To\:find:}$

• Length of the other parallel side of the Trapezium ?

Explanation :

• let the measure of the length of the other parallel side of the Trapezium be "x" .

we know that ,

$\sf\purple{Area\:of\: Trapezium = \dfrac{1}{2}\times ( a + b )\times h }$

here ,

• ( a + b ) is the sum of measures of the parallel side that is ( 25 + x ) .

• h is the height of the Trapezium that is 7 cm .

$\\ \longrightarrow\sf{ 140 = \dfrac{1}{2}\times ( 25 + x )\times 7}$

$\\ \longrightarrow\sf{ 140\times 2 = ( 25 + x )\times 7}$

$\\ \longrightarrow\sf{ 280 = ( 25 + x )\times 7}$

$\\ \longrightarrow\sf{ 280 = 175 + 7x }$

$\\ \longrightarrow\sf{ 280 - 175 = 7x }$

$\\ \longrightarrow\sf{ 105 = 7x }$

$\\ \longrightarrow\sf{ \dfrac{105}{7} = x }$

$\\ \longrightarrow\sf{ 15 = x }$

• Therefore the length of the other side of the Trapezium is 15 cm

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Answer 2

Question :

• Area of trapezium is 140cm². if length of one parallel side is 25 cm and the distance between them is 7cm, then find the length of other side.

Answer :

Given :-

• Area of Trapezium is 140 cm².

• Length of one parallel side is 25 cm.

• Distance between the two parallel sides is 7 cm.

To Find :-

• The length of other parallel line.

Formula Used :-

Let us consider a trapezium whose parallel sides are of length 'a' units and 'b' units and distance between paralkel sides be 'h' units then area of trapezium is

$\sf \: Area_{(trapezium)} = \dfrac{1}{2} (a + b) \times h$

Solution :-

Given that :-

• Area of Trapezium = 140 cm².

• Length of one parallel side, a = 25 cm.

• Distance between the two parallel sides, h = 7 cm.

• Let length of other parallel side = 'b' cm

We know,

$\rm :\longmapsto\: \sf \: Area_{(trapezium)} = \dfrac{1}{2} (a + b) \times h$

On substituting all the above values in this formula, we get

$\rm :\longmapsto\:140 = \dfrac{1}{2} (25 + b) \times 7$

$\rm :\longmapsto\:40 = 25 + b$

$\bf\implies \:b = 15 \: cm$

Hence,

• Length of other parallel side is 15 cm.

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Additional Information :-

$\boxed{ \bf{ \: Area_{(rectangle)} = length \times breadth}}$

$\boxed{ \bf{ \: Area_{(square)} = {(side)}^{2} }}$

$\boxed{ \bf{ \: Area_{(rhombus)} = \dfrac{1}{2} \times product \: of \: diagonals}}$

$\boxed{ \bf{ \: Area_{(right \: triangle)} = \dfrac{1}{2} \times base \times height}}$

$\boxed{ \bf{ \: Area_{(parallelogram)} = base \times height}}$

$\boxed{ \bf{ \: Area_{(equilateral \triangle)} = \dfrac{ \sqrt{3} }{4} {(side)}^{2} }}$