Question

Two parallel sides of the trapezium are
16 cm and 20 cm
If area is equal to
90 cm then what is the height of the
trapezium ?​

Answer 1

Given -

• Area of trapezium = 90cm²

• Parallel sides = 16cm and 20cm

To find -

• Measure of height.

Formula used -

• Area of Trapezium.

Solution -

In the question, we are provided with the, area and the two parallel sides of a trapeizium and we need to find out the measure of height. For that we will use the formula of area of trapezium, first we will name the height as h, then we will apply the formula of area of trapezium, after that we will obtain the height of the trapeizium. Let's do it!

So -

Let the height be termed as h

Area = 90cm²

two parallel sides = 16cm and 20cm

Area of trapezium = $\bf\dfrac{a + b}{2}$ × h

where -

a = 1st side

b = 2nd side

h = Height

On substituting the values -

$\tt \: area \: = \dfrac{a + b}{2} \times h \\ \\ \ \tt \: 90cm^{2} \: = \frac{16 + 20}{2} \times h \\ \\ \tt \: h \: = 2 \times \frac {90\:cm}{16\:cm+ 20\:cm} \\ \\ \tt h \: = 2 \times \: \frac{90\:cm}{36\:cm} \\ \\ \tt \: h \: = 2 \times 2.5\:cm \\ \\ \bf \: h = 5cm$

$\therefore$ The height of the trapeizium is 5cm

Verification -

area = $\tt\dfrac{a + b}{2} \times h$

90cm² = $\tt\dfrac{16 + 20}{2} \times 5$

90cm² = $\tt\dfrac{36}{2} \times 5$

90cm² = 18 × 5cm

90cm² = 90cm²

Hence verified

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Answer 2

Answer:

Given :-

• Two parallel sides of a trapezium is 16 cm and 20 cm and the area of a trapezium is 90 cm.

To Find :-

• What is the height of a trapezium.

Formula Used :-

$\sf\boxed{\bold{\small{Area\: of\: trapezium\: =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides\: \times Height}}}$

Solution :-

Let, the height of a trapezium be h

Given :

• Two parallel sides = 16 cm and 20 cm
• Area of trapezium = 90 cm

According to the question by using the formula we get,

⇒ 90 = $\sf\dfrac{1}{2} \times (16 + 20) \times h$

⇒ 90 = $\sf\dfrac{1}{2} \times 36 \times h$

⇒ 90 = $\sf\dfrac{1}{\cancel{2}} \times {\cancel{36}} \times h$

⇒ 90 = $\sf 18 \times h$

⇒ $\sf\dfrac{\cancel{90}}{\cancel{18}}$ = h

⇒ 5 = h

➠ h = 5 cm

$\therefore$ The height of a trapezium is 5 cm .

$\rule{150}{2}$

VERIFICATION :-

↦ 90 = $\sf\dfrac{1}{2} \times (16 + 20) \times h$

Put h = 5 we get,

↦ 90 = $\sf\dfrac{1}{2} \times (16 + 20) \times 5$

↦ 90 = $\sf\dfrac{1}{2} \times 36 \times 5$

↦ 90 = $\sf\dfrac{1}{2} \times 180$

↦ 90 = $\sf\dfrac{1}{\cancel{2}} \times {\cancel{180}}$

↦ 90 = 90

➦ LHS = RHS

Hence, Verified ✔