Question

Q4 Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.​

Answer 1

Attachment ⤴️⤴️⤴️⤴️⤴️

Question ⤵️⤵️

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides

AD and BC.

Answer⤵️⤵️

660m²

Answer 2

Given Question :-

• Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

ANSWER

GIVEN :-

A trapezium ABCD having

• Perimeter = 120 m

• BC = 48 m, CD = 17 m and AD = 40 m,

• Side AB is perpendicular to the parallel sides AD and BC.

TO FIND :-

• AREA OF TRAPEZIUM

FORMULA USED

$\boxed{ \bf Area_{(trapezium)} \: = \dfrac{1}{2} \bigg( sum \: of \: \parallel \: sides \bigg) \times height}$

CALCULATION :-

Given that,

• Perimeter of Trapezium = 120 m

So,

it implies

• AB + BC + CD + DA = 120

• AB + 48 + 17 + 40 = 120

• AB + 105 = 120

• AB = 15 m

Now,

• In trapezium ABCD,

• AD and BC are || lines and height of trapezium is AB.

Now,

• AD = 40 m

• BC = 48 m

and

• AB = 15 m

So,

• Area of trapezium is evaluated as

$\longmapsto \red{ \bf \:Area_{(trapezium)} = \dfrac{1}{2}(AD + BC) \times AB }$

$\rm :\implies\:Area_{(trapezium)} = \dfrac{1}{2} (40 + 48) \times 15$

$\rm :\implies\:Area_{(trapezium)} = \dfrac{1}{2} \times 88 \times 15$

$\rm :\implies\:Area_{(trapezium)} = 44 \times 15$

$\rm :\implies\: \large \boxed{\red{ \bf \: Area_{(trapezium)} = 660 \: {m}^{2} }}$