Question

The parallel sides of trapezium are 40 cm and 70 cm. Its non parallel sides are equal 25 cm each. Find area of trapezium..

Answer 1

I hope this will help you

Answer 2

Area of Trapezium is 1100 sq.cm.

Step-by-step explanation:

We have drawn the diagram for your reference.

Given:

The parallel sides of trapezium are 40 cm and 70 cm.

hence according to diagram:

AD = 40 cm

BC = 70 cm

Also Given:

Its non parallel sides are equal 25 cm each.

AB = 25 cm

CD =25 cm

So first we will draw imaginary lines AE and DF which are perpendicular BC such that;

EF = AD = 40 cm

so,

BE = FC = 15 cm each

Now In triangle Δ AEB.

m∠E = 90°

Hence By Pythagoras theorem we get;

$AE^2+BE^2= AB^2$

Substituting the values we get;

$AE^2+ 15^2 = 25^2\\\\AE^2 + 225 =625\\\\AE^2 = 625-225\\\\AE^2 =400$

Now Taking Square root on both side we get;

$\sqrt{AE^2} =\sqrt{400} \\\\AE =20\ cm$

Now we need to find the Area of trapezium.

Area of trapezium is equal to half times sum of parallel side times distance between them.

framing in equation form we get;

Area of trapezium = $\frac{1}{2}\times AE \times (AD+BC) = \frac{1}{2}\times 20\times (40+70) = 1100 \ cm^2$

Hence Area of Trapezium is 1100 sq.cm.