A park in the shape of a quadrilateral

ABCD
has AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and

c=

90
°

. The area of the park is ____

m
2

. [Given:

35

=5.9
]

Question

A park in the shape of a quadrilateral

ABCD
   has AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and

c=
    
     90
    °

. The area of the park is ____

m
    2

. [Given:

35
   
   =5.9
  ]

Accepted Answer

A park in the shape of a quadrilateral

ABCD
   has AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and

C=
    
     90
    °

. The area of the park is 65.4

m
    2

.Given a quadrilateral

ABCD
   with AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and

C=
    
     90
    °

.As BCD is a right-angled triangle, using Pythagoras theorem,

hypotenuse
      
      2
     
     =

base
      
      2
     
     +

perpendicular
      
      2

⇒hypotenuse=

base
         
        2
       
       +

perpendicular
         
        2

⇒BD

=

B
          C
          2
         
         +C
          D
          2

⇒BD

=

12
          2
         
         +
          5
          2

⇒BD

=

169

⇒BD

=

13m

Now area of

Δ
  BCD is,

Area of triangle= 
    1
    2
   
   ×base×height

⇒Area of ΔBCD=
      1
      2
     
     ×BC×CD

⇒Area of ΔBCD=
      1
      2
     
     ×12×5

⇒Area of ΔBCD=30
      m
      2

The value of semi perimeter (s) for

Δ
  ABD is,

s

=

a+b+c
        2

⇒s

=

9+8+13
        2

⇒s

=

15m

Now, using Heron’s formula in triangle ABD

⇒Area of ΔABD=
      
       s
        
         s−a

s−b

s−c

⇒Area of ΔABD=
      
       15
        
         15−9

15−8

15−13

⇒Area of ΔABD=3×2
      
       35

⇒Area of ΔABD=35.4
      m
      2

Overall area of quadrilateral is,

⇒Area of ABCD= 30 + 35.4

⇒Area of ABCD= 65.4 
      m
      2

The area of the park is

65.4
    m
    2

.

A park in the shape of a quadrilateral $ABCD$ has AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and $c = 90 °$ . The area of the park is ____ $m 2$ . [Given: $35 = 5.9$ ]

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

A park in the shape of a quadrilateral ABCD has AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and c= 90 ° . The area of the park is ____ m 2 . [Given: 35 =5.9 ]