Question

the area of a trapezium is 34 cm² and the length of one of the parallel sides is 10 cm and its height is 4 cm find the length of the Other parallel sides​

Answer 1

Answer:

Given :-

• The area of a trapezium is 34 cm² and the length of one of the parallel sides is 10 cm and height is 4 cm.

To Find :-

• What is the other parallel sides.

Formula Used :-

$\clubsuit$ Area Of Trapezium Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Trapezium)} =\: \dfrac{1}{2} \times (Sum\: of\: Parallel\: Sides) \times Height}}}\: \: \: \bigstar$

Solution :-

Let,

$\small \mapsto \bf Other\: Parallel\: sides_{(Trapezium)} =\: b\: cm$

Given :

• Area of Trapezium = 34 cm²
• One parallel sides = 10 cm
• Height = 4 cm

According to the question by using the formula we get,

$\footnotesize \implies \bf Area_{(Trapezium)} =\: \dfrac{1}{2} \times (Sum\: of\: Parallel\: Sides) \times Height$

$\implies \sf 34 =\: \dfrac{1}{2} \times (10 + b) \times 4$

$\implies \sf 34 \times \dfrac{2}{1} =\: (10 + b) \times 4$

$\implies \sf \dfrac{34 \times 2}{1} =\: (10 + b) \times 4$

$\implies \sf \dfrac{68}{1} =\: (10 + b) \times 4$

$\implies \sf 68 =\: (10 + b) \times 4$

$\implies \sf 68 \times \dfrac{1}{4} =\: 10 + b$

$\implies \sf \dfrac{68 \times 1}{4} =\: 10 + b$

$\implies \sf \dfrac{\cancel{68}}{\cancel{4}} =\: 10 + b$

$\implies \sf \dfrac{17}{1} =\: 10 + b$

$\implies \sf 17 =\: 10 + b$

$\implies \sf 17 - 10 =\: b$

$\implies \sf 7 =\: b$

$\implies \sf\bold{\blue{b =\: 7}}$

Hence, the required length of the other parallel sides of a trapezium :

$\small \dashrightarrow \sf Other\: Parallel\: Sides_{(Trapezium)} =\: b\: cm$

$\small \dashrightarrow \sf\bold{\red{Other\: Parallel\: Sides_{(Trapezium)} =\: 7\: cm}}$

$\small \sf\bold{\purple{\underline{\therefore\: The\: length\: of\: other\: parallel\: sides\: of\: trapezium\: is\: 7\: cm\: .}}}$

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