Question

The parallel sides of a trapezium are 40 cm and 20 cm. Find the area of trapezium if its non parallel sides are equal and have lenght is 26 cm.​

Answer 1

Answer:

area of the trapezium = 1/2 × h × (b1 + b2)

= 1/2 × 26 × (20 + 40)

= 1 × 13 × 60

= 780cm²

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Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Parallel sides of a Trapezium are 40 cm & 20 cm

✭ Length of the non parallel sides are equal with a length of 26 cm

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The area of the trapezium?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here consider a Trapezium with,

• AB = 40 cm
• DC = 20 cm
• BC = 26 cm
• AD = 26 cm

Draw a CE ⟂ AB

Which means that,

➝ $\displaystyle\sf FB = AB-AF$

➝ $\displaystyle\sf FB = 40-20 = \green{20 \ cm}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

In ∆FBC

⪼ $\displaystyle\sf BC = FC$

$\displaystyle\sf \therefore$ ∆FBC is an Isosceles triangle

As E is the mid point of FB

$\displaystyle\sf:\implies FE = \dfrac{1}{2} FB$

$\displaystyle\sf:\implies FE = \dfrac{1}{2}\times 20$

$\displaystyle\sf:\implies\green{FE = 10 \ cm}$

In ∆CEF

Using pythagoras theorem,

$\displaystyle\sf\twoheadrightarrow CF^2 = FE^2+CE^2$

$\displaystyle\sf\twoheadrightarrow 26^2 = 10^2+CE^2$

$\displaystyle\sf\twoheadrightarrow 676=100+CE^2$

$\displaystyle\sf\twoheadrightarrow 676-100 = CE^2$

$\displaystyle\sf\twoheadrightarrow 576 = CE^2$

$\displaystyle\sf\twoheadrightarrow \sqrt{576} = CE$

$\displaystyle\sf\twoheadrightarrow \orange{CE = 24 \ cm}$

Now that we have the Height and the parallel sides we can find the area of the trapezium with the help of,

$\displaystyle\underline{\boxed{\sf Ar_{Trapezium} = \dfrac{Sum \ of parallel \ sides}{2} \times Height}}$

Substituting the values,

$\displaystyle\sf\dashrightarrow Ar = \dfrac{40+20}{2} \times 24$

$\displaystyle\sf\dashrightarrow Ar = \dfrac{60}{2} \times 24$

$\displaystyle\sf\dashrightarrow Ar = 30\times 24$

$\displaystyle\sf\dashrightarrow\pink{Ar = 720 \ cm^2}$

$\sf\star\: Diagram\:\star$

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