Question

the area of trapezium is equal to 180 cm find the height of the trapezium if its parallel sides are 25 cm and 15 CM​

Answer 1

Given :

• Area of the Trapezium = 180 cm²

• Parallel side ($p_{1}$) = 25 cm

• Parallel side ($p_{2}$) = 15 cm

To Find :

The height of the Trapezium !

Solution :

Let the height of the Trapezium be h cm.

We know that the area of an Trapezium is :

$\underline{\boxed{\bf{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h}}}$

⠀⠀⠀⠀⠀⠀⠀Where :-

⠀⠀⠀⠀A = Area of the Trapezium

⠀⠀⠀⠀⠀h = Height of the Trapezium

⠀⠀⠀⠀ ⠀p = Parallel sides

Now , using the above formula and substituting the values in it , we get :-

$:\implies \bf{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h} \\ \\ \\ :\implies \bf{180 = \dfrac{1}{2} \times (25 + 15) \times h} \\ \\ \\ :\implies \bf{180 = \dfrac{1}{2} \times 40 \times h} \\ \\ \\ :\implies \bf{180 \times 2 = 40 \times h} \\ \\ \\ :\implies \bf{360 = 30 \times h} \\ \\ \\ :\implies \bf{\dfrac{360}{40} = h} \\ \\ \\ :\implies \bf{9 = h} \\ \\ \\ \therefore \bf{height = 9 cm}$

Hence, the height of the Trapezium is 9 cm.

Answer 2

☯️ Given :-

• Area Of Trapezium = 180cm²

• Parallel Side (1) = 25cm.

• Parallel Side (2) = 15cm.

☯️ To Find :-

• Height Of Trapezium.

☯️ Solution :-

We Know that,

Area of Trapezium :-

$\sf { \dfrac{1}{2} \times (p1 + p2 ) \times height}$

Now, Put the values.

$\implies\sf{ \dfrac{1}{2} \times (25 + 15) \times Height = 180}$

$\implies\sf{ \dfrac{1}{\cancel{2}} \times {\cancel{40}} \: \: ^{20} \times Height \: = 180}$

$\implies \sf{20 \times Height \: = 180}$

$\implies\sf{Height = \cancel{\dfrac{180}{20}} \: \: 9 }$

$\implies\boxed{\bf\red{Height = 9cm}}$

Hence, The Required Height = 9cm.