Question

The parallel sides of a trapezium are 20cm and 13cm. It's non-parallel side are 10 cm each. Find the area of Trapezium. ​

Answer 1

Answer:

here is your answer...hope it helps you...

Answer 2

Given :-

• Length of Parallel side = 20 cm

• Length of Other parallel side = 13 cm

• Length of Non parallel side = 10 cm

To Find :-

• Area of the trapezium.

Solution :-

Let the trapezium be ABCD.

Draw parallel line to BC ,

$\dashrightarrow\:\:\rm{BC = AE = 10cm}$

Draw another line which perpendicular to DC

Now,

$\dashrightarrow\:\:\rm{AB = EC = 13cm}$

$\dashrightarrow\:\:\rm{DE = 20 -13 =7cm}$

AF is perpendicular to DC it divides DF, and FE equally

So,

$\dashrightarrow\:\:\rm{DF = FE = \dfrac{7}{2} }$

$\dashrightarrow\:\:\rm{DF = FE=3.5cm }$

AFE triangle and AFD triangle are right angled triangle.

$:\implies\:\rm{AF^2 + FE^2=AE^2 }$

$:\implies\:\rm{AF^2 + 3.5^2=10^2 }$

$:\implies\:\rm{AF^2 + 12.25=100 }$

$:\implies\:\rm{AF^2 = 100-12.25 }$

$:\implies\:\rm{AF^2 = 87.75 }$

$:\implies\:\rm{AF = \sqrt{87.75 } }$

$\sf:\implies \underline{\boxed{\pink{\textbf{AF=9.36}}}}\:\:\bigstar$

∴ Height of AF = 9.3 cm

We know that,

$\bullet\:\:\underline{\boxed{\bf{Area\:of\:trapezium = \dfrac{1}{2}\times h \times (a+b) }}}$

Here,

• h = 9.3 cm

• a = 20 cm

• b = 13 cm

Now,

$:\implies\:\sf{\dfrac{1}{2}\times 9.3 \times (20 + 13) }$

$:\implies\:\sf{\dfrac{1}{2} \times 9.3 \times (33) }$

$:\implies\:\sf{\dfrac{33 \times 9.3}{2} }$

$:\implies\:\sf{\dfrac{306.2}{2} }$

$\sf:\implies \underline{\boxed{\pink{\mathfrak{1653.45\:cm^2}}}}\:\:\bigstar$

∴ Area of the trapezium = 1653.45 cm²

Hope it helps uh, Sara here ! :D