Question

the area of a trapezium shaped feild is 450m²distance between two parrell sides is 15m and of the parrell side 25m find the other parrell side​

Answer 1

$\frak{Given}\begin{cases}\sf{\:\;\;Area\;of\; trapezium\;field=\:\bf{450\;m^2}}\\\sf{\;\;\; Distance\;b/w\;two\;||\; sides= \bf{15\;m}}\\\sf{\:\;\;One\;of\; parallel\:side=\bf{25\;m}}\end{cases}$

Need to find: The other parallel side.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

❍ Let the one of the parallel side of the trapezium field be b cm respectively.

$\underline{\frak{Diagram:}}$

$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf B }\put(-0.3,-0.3){ \bf D }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 15\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 20\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf ?\ cm }\end{picture}$⠀⠀

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

⭑The Area of trapezium is given by :

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

Where,

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

$\dag\;{\underline{\frak{Now,\: Substituting\:values\:in\;formula,}}}$

$:\implies\sf 450 = \dfrac{1}{2}(20 + b) \times 15 \\\\\\:\implies\sf 450 \times 2 = (20 + b)\times 15 \\\\\\:\implies\sf 900 = (20 + b) \times 15\\\\\\:\implies\sf 900 = 300 + 15b\\\\\\:\implies\sf 900 - 300 = 15b\\\\\\:\implies\sf 600 = 15b \\\\\\:\implies\sf b = \cancel\dfrac{600}{15}\\\\\\:\implies{\underline{\boxed{\frak{\pink{b = 40\;m}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;the\;other\; parallel\;side\;is\;\bf{ 40\;m}.}}}$

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Answer 2

Given

• Area of trapezium shaped field = 450 m²
• Distance between parallel sides = 15 m
• One of the parallel side = 25 m

To find

• The other parallel side

Solution

Area of trapezium = 1/2 × (a + b) × h

Where :-

• a and b are parallel sides
• h is distance between two parallel sides

Substituting we get :-

• 450 = 1/2 (20 + b) × 15
• 450 × 2 = (20 + b) × 15
• 900 = (20 + b) × 15
• 900 = 300 + 15b
• 900 - 300 = 15b
• 600 = 15b
• b = 600/15
• b = 40

Hence, the other parallel side of trapezium is 40 m.