Question

surface area and volumes :-

class 10 cbse

In the figure, ABCD is a trapezium with AB || DC and angle BCD = 30 degree. If BGEC is a sector of a circle withcentre C and AB = BC = 7 cm,
DE = 4 cm and BF = 3.5 cm, then find the area of the shaded region

Answer 1

BC=7cm
therefore EC= BC= 7cm
area of sector BEC= 30/360 into 22/7 into 7 into 7
=12.8cm [approx]
area of trapezium = AB+DC/2 into BF
=31.5cm
therefore area of shaded region= area of trapezium - area of sector
31.5 - 12.8 =18.7 [approx]

Answer 2

Hey !!

Here is your answer....

Area of shaded region = Area of Trapezium ABCD - Area of sector BGEC

AB = BC = 7 cm
BC = EC = 7 cm. ....... ( radius )
DC = DE + EC
DC = 4 + 7
DC = 11 cm.

Area of Trapezium ABCD = AB + DC/2 × h
= 7 + 11/2 × 3.5
= 9 × 3.5
= 31.5 cm^2

Area of sector BGEC = theta πr^2
= 30/360 × 22/7 × 3.5 × 3.5
= 1/12 × 22 × 0.5 × 3.5
= 3.20 cm^2

Now,
Area of shaded region = 31.5 - 3.20
= 28.3 cm^2


Hope it helps you...

Thanks ^-^