Question

the length of parallel side a trapezium
are 30m and 50m. If the third
side is perpendicalar to parallel
sides and the length of fourth
side is 25m, then the area of
trapezium -​

Answer 1

Answer:

600 m²

Step-by-step explanation:

Given,

AB = 30 m

CD = 50 m

BC = 25 m

AD ⊥ CD and AD ⊥ AB

Construction required = Draw AE such that AE║BC and AE = 25 m and  CE = 30 m and ED = 20 m.

Now in rtΔ ADE using Pythagoras theorem we get,

= AD = √625 - 400

        = √225 = 15 m

Are of a trapezium = 1/2 x sum of parallel sides x distance between them

= 1/2 x (30 + 50) x 15 m²

= 40 x 15 m²

= 600 m²

Answer 2

AnswEr :

$\bf{\large{\underline{\rm{Given\::}}}}$

The length of parallel side a trapezium are 30 m and 50 m. If the third side is perpendicular to parallel sides and the length of fourth side is 25 m.

$\bf{\large{\underline{\rm{To\:find\::}}}}$

The area of trapezium.

$\bf{\Large{\underline{\tt{\orange{Explanation\::}}}}}$

Above given attachment a 'figure' according to question :

$\bf{\large{\underline{\underline{In\:\triangle BEC\::}}}}}$

Using Pythagoras theorem :

$\mathfrak{Given}\begin{cases}\sf{Base\:of\:\triangle\:=\:20m}\\ \sf{Hypotenuse\:of\:\triangle\:=\:25m}\\ \sf{Perpendicular\:of\:\triangle\:=\:?}\end{cases}}$

$\implies\tt{(Hypotenuse)^{2} \:(H)=(Perpendicular)^{2} \:(P)+(Base)^{2} \:(B)}\\\\\\\implies\tt{(25\:m)^{2} =P^{2} +(20\:m)^{2} }\\\\\\\implies\tt{P^{2} =(25m)^{2} -(20m)^{2} }\\\\\\\implies\tt{P^{2} =625m^{2} -400m^{2} }\\\\\\\implies\tt{P^{2} =225m^{2} }\\\\\\\implies\tt{P\:=\:\sqrt{225m^{2} } }\\\\\\\implies\tt{\red{P\:=\:15\:m}}$

∴ The height of trapezium is (BE) = 15 m.

Now,

Formula use :

$\bf{\large{\boxed{\sf{Area\:of\:trapezium\:=\:\frac{1}{2 }*(Sum\:of\:parallel\:sides)*height}}}}}}$

$\longrightarrow\tt{Area\:of\:trap.=\dfrac{1}{2} *(sum\:of\:parallel\:side)*height}\\\\\\\\\longrightarrow\tt{Area\:of\:trap.=\bigg[\dfrac{1}{2} *(30+50)*15\bigg]m^{2} }\\\\\\\\\longrightarrow\tt{Area\:of\:trap.=\bigg[\frac{1}{\cancel{2}} *\cancel{80}*15\bigg]m^{2} }\\\\\\\\\longrightarrow\tt{Area\:of\:trap.=\big(40*15\big)m^{2} }\\\\\\\\\longrightarrow\tt{\orange{Area\:of\:trap.\:=\:600\:m^{2} }}$

∴ The area of trapezium is 600 m².