ABCD is a piece of cardboard in the shape
of a trapezium in which AB || DC, ZABC 90°.
From this piece, quarter circle BEFC is removed.
Given DC = BC = 4.2 cm and AE = 2 cm.
Calculate the area of the remaining piece of the cardboard.
Answers
Answered by
5
Given BEFC is a quarter circle.
Thus, BC=BE= radius of the circle
BC=BE=DC=4.2 cm .... [Given]
Now, AB=AE+BE
=2+4.2
=6.2 cm
ABCD is trapezium AB∣∣CD and ∠ABC=90
Thus, area of trapezium ABCD=(
2
AB+CD
)×BC
=
2
6.2+4.2
×4.2
=21.84cm
2
Area of the quarter circle =
4
π(BC)
2
=
4
7
22
×(4.2)
2
=
7×4
22×17.64
=13.86cm
2
Thus, area of the shaded region =(21.84−13.86)cm
2
=7.98cm
2.
Similar questions