Question

In quadrilateral ABCD AB || DC and AD 1 AB. Also, AB = 8 m,
=BC=5 m. Find the area of the quadrilateral.
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Answer 1

Answer:

In quadrilateral ABCD:

Assume CE is a perpendicular dropped to AB,

Now we have a right angled △ CEB and a rectangle AECD

∴ Area of quadrilateral ABCD = Area of right angled △ CEB + Area of rectangle AECD

AB=AE+EB

EB=AB-AE = 8-5 = 3m (∵ AE=DC , opposite sides of a rectangle)

In △ CEB:

CB

2

= CE

2

+ EB

2

CE

2

= CB

2

- EB

2

CE

2

= 5

2

- 3

2

= 25-9=16

CE =

1

6 = 4m

Now, Area of △ CEB =

2

1

×3×4 = 6m

2

Area of rectangle AECD = DC × CE = 5 × 4 =20m

2

Area of quadrilateral ABCD = 6 m

2+ 20m 2

= 26m

2