Question

the parallel side of trapezium are 20 cm and 10 cm. it nonparallel side are both equal each being 13 cm. find the area of trapezium​

Answer 1

Answer:

Step-by-step explanation:

The answer is down side with expalnation.

Answer 2

In this Figure
Given
AB=10 cm
CD=20 cm

AC=BD=13 cm

AB perpendicular CD

Now When We make BED Triangle on Trapezium.
AB=10cm
CE=10 cm
AC=13 cm
BE=13 cm

Now in Triangle BED

Given Height=BF
Hypotenuse=13 cm

Now as CE=10 cm
CD=20 cm

ED=CD-CE
=20-10
=10 CM

EF=FD
ED=10 CM
FD=10-EF
=10-5
=5 CM

WE have got now
In Triangle BED

Base=5 cm
Hypotenuse=13 cm

Using Phythagoras Theroem
${bf}^{} = \sqrt{hypotenuse {}^{2} - base {}^{2} } \\ = bf = \sqrt{ {13}^{2} - {5}^{2} } \\ = bf = \sqrt{169 - 25} \\ bf = \sqrt{144} \\ bf = 12$
BF (height)=12 cm

Area of Trapezium
$\frac{1}{2} \times (ab + cd) \times \: height \\ = \frac{1}{ \cancel2} \times (10 + 20) \times \cancel 12 \\ = 30 \times 6 \\ = 180 \: {cm}^{2}$

$\boxed{\mathbf{Area\: \:of \:Trapezium={180\:cm}^{2}}}$