Question

The perimeter of trapezium shown in Fig. 13.13 is 120 m. If BC = 48 m, CD = 17 m B
and AD = 40 m, find the area of this field. It is given that side AB is perpendicular to the
parallel sides AD and BC.
​

Answer 1

Given: The perimeter of trapezium is 120 m.

And,  Length of sides BC, CD and AD is 48 m, 17 m and 40 m respectively.

To find: Area of trapezium field?

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❍ AB is perpendicular to the parallel sides AD and BC.

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

$\star\:{\boxed{\sf{\pink{Perimeter_{\:(trapezium)} = a + b + c + d}}}}$

Where,

• a, b, c and d are the sides of trapezium.

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$\dag\:{\underline{\frak{Putting\:values\:in\:formula\::}}}\\\\\\ :\implies\sf AB + BC + CD + DA = 120\\\\\\ :\implies\sf AB + 48 + 17 + 40 = 120\\\\\\ :\implies\sf AB + 105 = 120\\\\\\ :\implies\sf AB = 120 - 105\\\\\\:\implies{\underline{\boxed{\frak{\purple{AB = 15\:m}}}}}$

$\therefore\:{\underline{\sf{Height\:of\:trapezium\:field\:is\: {\textsf{\textbf{15\:m}}}.}}}$

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▪︎Now, Finding Area of trapezium field,

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

Where,

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

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$\dag\:{\underline{\frak{Putting\:values\:in\:formula\::}}}\\\\\\ :\implies\sf Area_{\:(field)} = \dfrac{1}{2} \times (AD + BC) \times AB\\\\\\ :\implies\sf Area_{\:(field)} = \dfrac{1}{2} \times (40 + 48) \times 15\\\\\\ :\implies\sf Area_{\:(field)} = \dfrac{1}{\cancel{2}} \times \cancel{88} \times 15\\\\\\ :\implies\sf Area_{\:(field)} = 44 \times 15\\\\\\ :\implies{\underline{\boxed{\frak{\purple{Area_{\:(field)} = 660\:m^2}}}}}$

$\therefore\:{\underline{\sf{Hence,\:Area\:of\:trapezium\:field\:is\: \bf{660\:m^2}.}}}$

Answer 2

$\huge \bf Given$

The perimeter of trapezium is 120 m.

, Length of sides BC, CD and AD is 48 m, 17 m and 40 m respectively.

$\huge \bf To \: Find$

Area

$\huge \bf Solution$

As we know that

Perimeter = a + b + c + d

120 = 48 + 17 + 40 + d

120 = 105 + d

d = 120 - 105

d = 15 m

Height = 15 m

Now,

Area of trapezium = ½ × (a + b) × h

Area = ½ × (40 + 48) × 15

Area = ½ × 88 × 15

Area = 1 × 44 × 15

Area = 44 × 15

Area = 660 m ²