Question

4.
If the area of a trapezium is 28 m2, and two parallel sides are 8 m and 60 dm
respectively, find the altitude.
5.
Find the height of a trapezium whose area is 1,080 cm2 and lengths of its parallel
sides are 55.6 cm and 34.4 cm.
its​

Answer 1

For 1 :

Given :

• Area of Trapezium is 28 m² .
• Length of the parallel sides are 8 m and 60 dm .

To Find :

• Altitude / Height

Solution :

$\longmapsto\tt{Parallel\:Sides=8\:m\:and\:60\:dm\:i.e. 6\:m}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{28=\dfrac{1}{2}\times{(8+6)}\times{h}}$

$\longmapsto\tt{28=\dfrac{1}{{\cancel{2}}}\times{{\cancel{14}}}\times{h}}$

$\longmapsto\tt{28=7\:h}$

$\longmapsto\tt{h=\dfrac{28}{7}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{h}\orange{=}\purple{4\:m}}}$

So , The Altitude/Height is 4 m .

_____________________________

For 2 :

Given :

• Area of Trapezium is 1080 cm² .
• Length of the parallel sides are 55.6 cm and 34.4 cm .

To Find :

• Altitude / Height

Solution :

$\longmapsto\tt{Parallel\:Sides=55.6\:cm\:and\:34.4\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{1080=\dfrac{1}{2}\times{(55.6+34.4)}\times{h}}$

$\longmapsto\tt{1080=\dfrac{1}{{\cancel{2}}}\times{{\cancel{90}}}\times{h}}$

$\longmapsto\tt{1080=45\:h}$

$\longmapsto\tt{h=\dfrac{1080}{45}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{h}\orange{=}\purple{24\:cm}}}$

So , The Altitude/Height is 24 cm .

Answer 2

Question:-

• If the area of a trapezium is 28 m2, and two parallel sides are 8 m and 60 m respectively, find the altitude.

To Find:-

• Find the height.

Formula to be Used:-

• $\sf \: Area = \dfrac { 1 } { 2 } \times ( Sum \: of \: parallel \: Sides )h$

Solution:-

$\sf\longrightarrow \: 28 = \dfrac { 1 } { 2 } \times ( 8 + 6 )h$

$\sf\longrightarrow \: 28 = \dfrac { 1 } { 2 } \times 14 \times h$

$\sf\longrightarrow \: 28 = 7h$

$\sf\longrightarrow \: h = \cancel\dfrac { 28 } { 7 }$

$\sf\longrightarrow \: h = 4$

Hence ,

• Height is 4 m.

Question:-

• Find the height of a trapezium whose area is 1,080 cm² and lengths of its parallel sides are 55.6 cm and 34.4 cm.

To Find:-

• Find the height.

Formula to be Used:-

• $\sf \: Area = \dfrac { 1 } { 2 } \times ( Sum \: of \: parallel \: Sides )h$

Solution:-

$\sf\longrightarrow \: 1080 = \dfrac { 1 } { 2 } \times ( 55.6 + 34.4 )h$

$\sf\longrightarrow \: 1080 = \dfrac { 1 } { \cancel 2 } \times \cancel { 90 } \times h$

$\sf\longrightarrow \: 1080 = 45h$

$\sf\longrightarrow \: h = \cancel\dfrac { 1080 } { 45 }$

$\sf\longrightarrow \: h = 24$

Hence ,

• Height is 24 cm