Question

The parallel sides of a Trapezium are 25 cm and 13 cm is non parallel sides are equal being 10 cm find the area of trapezium

Answer 1

Let ABCD be the given trapezium in which AB || DC, AB = 25 cm, DC = 13 cm
AD = BC = 10 cm.
Draw CL equal AB and CM || DA, meeting AB at L and M respectively.
Clearly, AMCD is a ||gm.
...AM = DC = 13 cm.
MB = (AB - AM) = (25 - 13) cm.
Now,CM = DA = 10 cm and CB = 10 cm.
... triangle CMB is an isosceles triangle and CL _| MB
=> L is the mid point of MB
=> ML = LB = (1/2*MB) = (1/2*12) cm = 6 cm.
From right triangle CLM, we have:
CL square = (CM square - ML square) ={(10)square - 6 square} cm square = (100 -36) cm square = 64 cm square
=> CL = √64 cm = 8 cm
height of the trapezium = 8 cm.

Answer 2

Hey Bro,

Ur answer is here

We have to find the area of trapezium.
Before going to calculation, let me make you remember the formula to calculate the area of trapezium. 
area of trapezium = half of height X sum of parallel sides.
In short,
$A = \frac{h(a+b)}{2}$

It is given that the parallel sides are 13 cm and 25 cm but the height of the trapezium is not given....

So, now let us first calculate the height of trapezium.

For seeing how to find the height. see the diagram I have uploaded as a picture....

Now see picture and then proceed from here......

Keeping in mind the information given in the picture,

AB = 13 cm
CD = 25 cm

As AD and BC are equal (i.e. 10 cm). 
So, by perpendicular construction of AE and BF, we can divide the side CD into the parts. 
In which EF = 13 cm (as AB = EF by construction).
and DE + CF = 25 - 13
= DE + CF = 12.
but DE and CF are equal as AD and BC are equal.

Hence, DE and CF are 6 cm.

We can see that ADE is 90°. So by applying Pythagoras theorem in ∆ ADE..

AD² = AE² + DE²
10² = AE² + 6²
AE² = 10² - 6²
AE² = 100 - 36
AE² = 64
AE = 8

Hence, AE = 8

Now, height is 8cm.

We can apply the formula, 
$A = \frac{h(a+b)}{2}$


Substituting values in the above formula,
$a = \frac{8(25+13}{2}$
= 4 (25+13)
= 4 X 38
= 152

Hence, the area of given trapezium is 152 cm².

Hope it helps......
#BRAINLY BENEFACTOR#