Question

the area of a trapezium is 440sq cm and length of parallel sides are 30 and 14 cm respectively finnd the height


with explanition

Answer 1

Answer:

20cm

Explanation:

We are given with,

• Area = 440cm²
• Two parallel sides 30cm and 14cm respectively.

We know,

Area of a trapezium = ½(a + b)h

Where,

• (a + b) denotes the sum of the parallel sides.
• h is the height.

Substitute the given values,

⇒ 440 = ½(30 + 14)h

⇒ 440 = ½(44)h

⇒ 440 = 22h

⇒ 440/22 = h

⇒ 20 = h

∴ Height of the trapezium is 20cm.

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$\:$

Answer 2

Answer:

Given :-

• The area of a trapezium is 440 cm² and the length of a parallel sides are 30 cm and 14 cm respectively.

To Find :-

• What is the height of a trapezium.

Formula Used :-

$\clubsuit$ Area Of Trapezium Formula :

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

Solution :-

Let,

$\mapsto \bf Height_{(Trapezium)} =\: h\: cm$

Given :

• Area of Trapezium = 440 cm²
• Parallel Sides = 30 cm and 14 cm

According to the question by using the formula we get,

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

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

$\implies \sf 440 =\: \dfrac{1}{2} \times (30 + 14) \times h$

$\implies \sf 440 \times \dfrac{2}{1} =\: 44 \times h$

$\implies \sf \dfrac{440 \times 2}{1} =\: 44 \times h$

$\implies \sf \dfrac{880}{1} =\: 44 \times h$

$\implies \sf 880 =\: 44 \times h$

$\implies \sf 880 \times \dfrac{1}{44} =\: h$

$\implies \sf \dfrac{880}{44} =\: h$

$\implies \sf 20 =\: h$

$\implies \sf\bold{h =\: 20}$

Hence, the required height of a trapezium is :

$\dashrightarrow \sf Height_{(Trapezium)} =\: h\: cm$

$\dashrightarrow \sf\boxed{\bold{\underline{Height_{(Trapezium)} =\: 20\: cm}}}$

$\therefore$ The height of a trapezium is 20 cm .