Question

Pls help me it's a difficult question don't give me irrevalant ans​

Answer 1

Given :

• Parallel Sides of a trapezium are 25 m and 10 m.
• Non-parallel sides are 14 m and 13 m

To Find :

• Area of Trapezium .

Solution :

• a = 13 m
• b = 14 m
• c = 15 m

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{\dfrac{13+14+15}{2}}$

$\longmapsto\tt{\cancel\dfrac{42}{2}}$

$\longmapsto\tt\bf{21\:m}$

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\dfrac{1}{2}\times{b}\times{h}=\sqrt{21(21-13)(21-14)(21-15)}}$

$\longmapsto\tt{\dfrac{1}{2}\times{15}\times{h}=\sqrt{21\:(8)\:(7)\:(6)}}$

$\longmapsto\tt{\dfrac{1}{2}\times{15}\times{h}=\sqrt{3\times{7}\times{2}\times{2}\times{2}\times{7}\times{2}\times{3}}}$

$\longmapsto\tt{\dfrac{1}{2}\times{15}\times{h}=3\times{2}\times{2}\times{7}}$

$\longmapsto\tt{\dfrac{1}{2}\times{15}\times{h}=84}$

$\longmapsto\tt{h=\dfrac{84\times{2}}{15}}$

$\longmapsto\tt{h=\cancel\dfrac{56}{2}}$

$\longmapsto\tt\bf{h=11.2\:m}$

So , The Height of Trapezium is 11.2 m ...

Now ,

$\longmapsto\tt{Height=11.2\:m}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{\dfrac{1}{2}\times{(10+25)}\times\dfrac{112}{10}}$

$\longmapsto\tt{\dfrac{1}{{\cancel{2}}}\times{{\cancel{35}}}\times\dfrac{{\cancel{112}}}{{\cancel{10}}}}$

$\longmapsto\tt{7\times{28}}$

$\longmapsto\tt\bf{196\:{m}^{2}}$

So , The Area of Trapezium is 196 m²..

Answer 2

Let ABCD be a trapezium with,

AB∥CD

AB=25m

CD=10m

BC=14m

AD=13m

Draw CE∥DA. So, ADCE is a parallelogram with,

CD=AE=10m

CE=AD=13m

BE=AB−AE=25−10=15m

In ΔBCE, the semi perimeter will be,

s= a+b+c/2

​

 

s=14+13+15/2

​

 

s=21m

Area of ΔBCE,

A= s(s−a)(s−b)(s−c)

​

 

= 21(21−14)(21−13)(21−15)

​

 

=\sqrt{x} 21(7)(8)(6)

​

 

=7056

​

 

=84m^2

 

Also, area of ΔBCE is,

A=1/2 ×base×height

84= 1/2 ×15×CL

84*2/15 = CL

CL= 56/5 m

Now, the area of trapezium is,

A= 1/2 (sum of parallel sides)(height)

A= 1/2 ×(25+10)( 56/5 )

A=196m^2  

 

Therefore, the area of the trapezium is 196m^2