In the figure below, UVWX and VWQP are squares. T and R are centres of square PQWV and UVWX respectively. S is the centre of VW. If UP = 42 m, take π as
227 and find
- the perimeter of the shaded region,
- the area of the shaded region.
(a)
Circumference of big circle
=
227 x 21
= 66 m
Circuference of four small semicircles
= 4 x
12 x
227 x 10.5
= 66 m
Circumference of two quadrants
=
14 x 2 x
227 x 21
= 33 m
Perimeter of the shaded region
= 66 + 66 + 33
= 165 m
(b)
Area of big circle
=
227 x 10.5 x 10.5
= 346.5 m
2Area of two shaded quadrant
=
12 x
227 x 10.5 x 10.5
= 173.25 m
2 Area of shaded region
= 346.5 + 173.25
= 519.75 m
2 Answer(s): (a) 165 m; (b) 519.75 m
2