Question

the area of a trapezium whose parallel sides are 10cm and 8cm where the perpendicular distance between the side is 4cm


please answer step by step ​

Answer 1

$\frak{Given} \begin{cases} & \sf{Distance\;b/w\;||\;sides = \bf{4\;cm}} \\ & \sf{One\:side\:of\:trapezium = \bf{10\:cm}} \\ & \sf{Other\:side\:of\:trapezium = \bf{8\:cm}} \end{cases}$

$\frak{To\:find:}$ The area of trapezium?

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⋆ DIAGRAM :

$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 4\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 10\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 8\ cm }\end{picture}$⠀⠀⠀⠀

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

To calculate the area of trapezium formula is given by :

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$\bf{\dag}\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}$

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Where,

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• a and b are the two parallel sides and h is distance between two parallel sides or height of trapezium.⠀⠀

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Now,

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$:\implies\sf Area_{trapezium} = \dfrac{1}{2} \times (10 + 8) \times 4 \\\\\\:\implies\sf Area_{trapezium} = \dfrac{1}{\cancel{\;2}} \times \;\cancel{18} \times 4 \\\\\\:\implies\sf Area_{trapezium} = 9 \times 4\\\\\\:\implies{\underline{\boxed{\frak{\pink{Area_{trapezium} = 36\;cm^2}}}}}\;\bigstar$

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$\therefore\:{\underline{\sf{Hence,\:The\:area\; of\; trapezium\;is\; \bf{36\;cm^2}.}}}$

Answer 2

To find :-

• Area of the trapezium .

Given :-

• 1st side of the trapezium is 10 cm
• 2nd side of the trapezium is 8 cm
• The distance between parallel sides is 4 cm

Solution :-

$\boxed{\red{\mathsf{Area\:of\:trapezium\:=\:\dfrac{1}{2}\:\times\:(A\:+\:B)\:\times\:h}}}$

• A as 1st  side = 10cm

• B as 2nd side = 8cm

• h  as parallel distance or height = 4cm

Here in the formula :-

1 ) a and b are two parallel sides .

2 ) h is the height of  the trapezium but according to the question we will take the height of the trapezium be distance of the two parallel side .

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↣ The area of a trapezium = 1/2 × ( A + B ) × h

↣ The area of a trapezium = 1/2 × ( 10 + 8 ) × 4

↣ The area of a trapezium = 1/2 × 18 × 4

↣ The area of a trapezium = 1 × 18 × 2

↣ The area of a trapezium = 36 centimeters ²

Therefore area of the trapezium is 36 cm² .