Math, asked by pawankumar9220, 11 months ago

In a quadrilateral abcd ab=40m bc=15 cd=28m ad=9m. find the area of the quadrilateral

Answers

Answered by ankita5786
4

Step-by-step explanation:

join ac then solve by Pythagoras theorem

then by find area

Answered by nahh2001
4

Step-by-step explanation:

AB =40 m

BC = 15 m

CD = 28 m

AD = 9 m

..

Join BD

..

(AB)² + (AD)² = (BD)²

(40)² + (9)² = (BD)²

1600 + 81 = (BD)²

1681 = (BD)²

BD = 41

..

Area of triangle ABD

..

a = 40 m

b = 9 m

c = 41 m

..

semi perimeter = a + b + c

—————

2

= 40 + 9 + 41

—————–—

2

= 90 ÷ 2

= 45m

..

Area = use heron's formula

= under root [ s ( s - a ) ( s - b ) ( s - c ) ]

= under root [ 45 ( 45 - 40 ) ( 45 - 9 ) ( 45 - 41 )]

= under root [ 45 × 5 × 36 × 4]

= 6 × 2 under root [ 9 × 5 × 5 ]

= 12 × 5 under root [ 9 ]

= 60 ×3

= 120 m² ............... ( 1 )

..

..

Area of triangle BDC

a = 15 m

b = 28 m

c = 41 m

..

semi perimeter = a + b + c

—————

2

15 + 28 + 41

= —————

2

= 84

——

2

= 42 m

..

..

Area = use heron's formula

= under root [ s ( s - a ) ( s - b ) ( s - c ) ]

= under root [ 42 ( 42 - 15 ) ( 42 - 28 ) ( 42 - 41 )

= under root ( 42 × 27 × 14 × 1 )

= under root (2× 3 × 7 × 3 × 3 × 3 × 7 × 2)

= 2 × 3 × 7 × 3

= 126 m² ......... ( 2 )

.

..

...

□ABCD = triangle ABD + triangle BDC

=120 m² + 126 m² = 246 m²

..

..

area of quadrilateral ABCD = 246 m²

.

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