Question

Two parallel sides of a trapezium are 58cm and 42 cm. The other two sides are of equal lengthb5cm, which is 17cm. Find the area of trapezium.​

Answer 1

Answer:

Area = 750cm²

Explanation:

Given,

Two parallel sides of a trapezium are :- 58cm and 42cm

And the other two sides are 5cm and 17cm.

We know that,

Area of a trapezium = ½(a + b)h

Where,

• a and b denotes the parallel sides.
• And, h is the height.

Let's calculate the height of the trapezium.

Construction :-

Let us draw two perpendicular lines AF and BE from the vertex A and B to line DC as shown in the figure.

Now, when the perpendicular lines are drawn

• AB = EF = 42cm.

Then remaining sides DF and EC would be,

$= \dfrac{58 - 42}{2}$

$= \dfrac{16}{2}$

$\rm = 8cm$

So we got, DF = EC = 8cm.

Applying Pythagoras theorem,

$\rm \implies \: {(BC)}^{2} = {(BE)}^{2} + {(EC)}^{2}$

$\rm \implies \: {(17)}^{2} = {(BE)}^{2} + {(8cm)}^{2}$

$\rm \implies \: 289 = {(BE)}^{2} + 64$

$\rm \implies \: 289 - 64 = {(BE)}^{2}$

$\rm \implies \: 225 = {(BE)}^{2}$

$\rm \implies \: \sqrt{ 225 }= {BE}$

$\rm \implies \: {BE} = 15cm$

So the height of the trapezium is 15cm.

Therefore, Area of the trapezium is :-

→ ½(58 + 42)*15

→ ½(100)*15

→ 50*15

→ 750cm²

∴ Area of the trapezium 750cm²