Question

Find the area of trapezium whose parallel sides are
of lengths 10cm and 12cm
and the distance between
them is 4 cm.​

Answer 1

Answer:

The area of the trapezium is 44 cm²

Step-by-step explanation:

Parallel sides of the trapezium = 10 cm and 12 cm.

Distance between the parallel sides = 4 cm

The distance between the parallel sides is actually the height of the trapezium.

We're given with:

• Side₁ = 10 cm
• Side₂ = 12 cm
• Height = 4 cm

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$\sf{\bigstar{\:Area\:of\:Trapezium = \dfrac{Side_{1} +Side_{2}}{2} \times h}$

$\longrightarrow\sf{\dfrac{(10+12)}{2} \times 4$

$\longrightarrow\sf{\dfrac{22}{2} \times 4$

$\longrightarrow\sf{22 \times 2}$

$\longrightarrow\sf{44}$

Area of trapezium = 44 cm²

Therefore, the area of the trapezium is 44 cm²

Answer 2

Given : The length of Parallel sides of Trapezium are 10 cm & 12 cm and the height or Distance between the parallel sides of the Trapezium is 4 cm .

Exigency To Find : The area of Trapezium.

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⠀⠀⠀⠀⠀⠀⠀⠀❍⠀Finding Area of Trapezium :

$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\\qquad\bigstar\:\bf\:Formula\:of\:Area\:of\:Trapezium\:\::$

$\qquad \dag\:\:\bigg\lgroup \sf{Area _{(Trapezium)} \:: \dfrac{1}{2} \times h \times ( a + b) }\bigg\rgroup$

⠀⠀⠀⠀⠀⠀Here , h is the Height or Distance between the parallel sides of Trapezium , a and b are the two parallel sides of Trapezium & ( a + b ) is the sum of the parallel sides of the Trapezium.

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Area _{(Trapezium)} \:= \dfrac{1}{2} \times h \times ( a + b)$

$\qquad:\implies \sf Area _{(Trapezium)} \:= \dfrac{1}{2} \times 4 \times ( 10 + 12)$

$\qquad:\implies \sf Area _{(Trapezium)} \:= \dfrac{1}{2} \times 4 \times ( 22)$

$\qquad:\implies \sf Area _{(Trapezium)} \:= \dfrac{1}{2} \times 4 \times 22$

$\qquad:\implies \sf Area _{(Trapezium)} \:= \dfrac{1}{\cancel {2}} \times \cancel {4} \times 22$

$\qquad:\implies \sf Area _{(Trapezium)} \:= 2 \times 22$

$\qquad:\implies \sf Area _{(Trapezium)} \:= 44$

$\qquad :\implies \frak{\underline{\purple{\: Area _{(Trapezium)} \:= 44\:cm^2 }} }\:\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Area \:of\:Trapezium \:is\:\bf{44\:cm^2}}.}}$

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