Question

Find the altitude of a trapezium whose area is 540 sq.m and the sum of its parallel sides is 36 m​

Answer 1

Answer:

30

Step-by-step explanation:

AREA OF TRAPEZIUM= 1/2H(SUM OF PARALLEL SIDES)

Let the altitude= x

x/2(36)=540

x(18)=540

x=540/18

x=30

Answer 2

The altitude of the trapezium is 30 m.

Step-by-step explanation:

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

• The area of a trapezium = 540 m²
• The sum of its parallel sides = 36 m

${\underline{\underline{\bf{Need\:to\: find:}}}}$

• The altitude of the trapezium

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{[Trapezium]}=\dfrac{1}{2}h(a+b)\:sq.units}}}$

$\:\:\:\:\:\:\:\:\:\:\sf{\bullet\:h=height}$

$\:\:\:\:\:\:\:\:\:\:\sf{\bullet\:a=parallel\: side\:_1}$

$\:\:\:\:\:\:\:\:\:\:\sf{\bullet\:b=parallel\:side\:_2}$

${\underline{\underline{\bf{Solution:}}}}$

As we know the measure of area of the trapezium, the altitude can be found by inserting the given measures in the formula below and by solving the equation.

$\leadsto{\sf{\purple{Area = \dfrac{1}{2}h(a+b)\:sq.units}}}$

$\:$

$\:\:\:\:\:\:\:\::\implies{\sf{540=\dfrac{1}{\cancel{2}}\times h\times \cancel{36}}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{540=h\times 18}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{\cancel{540}}{\cancel{18}}=h}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{\cancel{270}}{\cancel{9}}=h}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{\cancel{90}}{\cancel{3}}=h}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\boxed{\frak{\red{30\:m}=h}}}$

• Therefore, the altitude of the trapezium is 30 m.

________________________________________

${\underline{\underline{\bf{Some\: formulae\:for\:area:}}}}$

$\sf{\bullet\:{Area}_{[Square]}=s^2\:sq.units}$

$\sf{\bullet\:{Area}_{[Rectangle]}=lb\:sq.units}$

$\sf{\bullet\:{Area}_{[Parallelogram]}=bh\:sq.units}$

$\sf{\bullet\:{Area}_{[Rhombus]}=\dfrac{1}{2}d_1d_2\:sq.units}$

$\sf{\bullet\:{Area}_{[Circle]}=\pi r^2\:sq.units}$

$\sf{\bullet\:{Area}_{[Semi\: circle]}=\dfrac{1}{2}\pi r^2\:sq.units}$