Question

The area of trapezium is 12 m2. Height of the trapezium is 3 m and one of the parallel sides is 1 m
more than the other. Find the length of parallel sides of the trapezium.​

Answer 1

Required Solution:

Given:

• Area of trapezium = 12m²

• Height of the trapezium = 3m

• One of the parallel side is 1m more than the other.

To calculate:

• Length of the parallel sides

Calculation:

Let the one side of the parallel side of the trapezium be x.

$\therefore$ Another parallel side of trapezium = x + 1

Now we know that:

$\small \rm \red { Ar. \: of \: trap. = \dfrac{1}{2} \times (sum \: of \: parallel \: sides ) \times h }$

Substitute the values the find the value of x:

$\sf { ⇢ 12 = \dfrac{1}{2} \times (x + x+1) \times 3}$

$\sf { ⇢ 12 = \dfrac{1}{2} \times (2x+1) \times 3}$

$\sf { ⇢ 12 \times 2 = 1 \times (2x+1) \times 3}$

(Transposing 2 from RHS to LHS)

$\sf { ⇢ 24 = (2x+1) \times 3}$

$\sf { ⇢ \dfrac{24}{3} = (2x+1) }$

(Transposing 3 from RHS to LHS)

$\sf { ⇢ 8= 2x+1 }$

$\sf { ⇢ 2x = 8-1 }$

$\sf { ⇢ 2x = 7}$

$\sf \blue { ⇢ x = \dfrac{7}{2}m}$

Therefore,length of one side of of the parallel side of the trapezium be 7/2m.

Also,

• Length of another side of the trapezium =

$\sf { ⇢ \dfrac{7}{2} +1 }$

$\sf { ⇢ \dfrac{7+4}{2} }$

$\sf \blue { ⇢ \dfrac{9}{2}m }$

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Verification:

Substitute all the values in the formula of area of the trapezium,if RHS and LHS is equal then our answer is correct.

$\small \rm { Ar. \: of \: trap. = \dfrac{1}{2} \times (sum \: of \: parallel \: sides ) \times h }$

$\sf { ⇢ 12 = \dfrac{1}{2} \times \Bigg( \dfrac{7}{2} + \dfrac{9}{2} \Bigg) \times 3}$

$\sf { ⇢ 12 = \dfrac{1}{2} \times \cancel{ \dfrac{16}{2} } \times 3}$

$\sf { ⇢ 12 = \dfrac{1}{2} \times 8 \times 3}$

$\sf { ⇢ 12 = \dfrac{1}{\cancel{2}} \times \cancel{24} }$

$\sf { ⇢ 12 = 12}$

LHS = RHS.

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