Question

5. Find the area of the quadrilateral ABCD whose dimensions are : AB = 90 cm
BC = 96 cm, CD = 72 cm, AD = 70 cm and BD =120 cm.​

Answer 1

Answer:

253

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Answer 2

The area of quadrilateral ABCD whose dimensions are : AB = 90 cm  BC = 96 cm, CD = 72 cm, AD = 70 cm and BD =120 cm is given by,

Formulae being used are:

Side, s = (a + b + c)/2

Area = √ [ s (s-a) (s-b) (s-c) ]

Here, we divide a quadrilateral ABCD into 2 triangles Δ ABD and Δ BCD

In Δ ABD,

AB = 90 cm

BD = 120 cm

AD = 70 cm

s = (90 + 120 + 70)/2 = 140

Area = √ [ 140 (140 - 90) (140 - 120) (140 - 70) ]

= √ [ 140 (50) (20) (70) ]

= 3130.4 cm²

In Δ BCD,

BC = 96 cm

BD = 120 cm

CD = 72 cm

s = (96 + 120 + 72)/2 = 144

Area = √ [ 144 (144 - 96) (144 - 120) (144 - 72) ]

= √ [ 144 (48) (24) (72) ]

= 3456 cm²

Area of quadrilateral ABCD = Area of Δ ABD + Area of  Δ BCD

= 3130.4  + 3456

= 6586.4 cm²