Cambridge International Mathematics

Mensuration (length and area) (Chapter 9) 201

You should already be familiar with these terms relating to circles:

Acircleis the set of all points a fixed distance from a

point called the circle’scentre.

A line segment from the centre to any point on the circle

is called aradius.

We denote the length of the radius byr. The perimeter

of a circle is called itscircumference.

A line segment which joins any two points on the circle

is called achord.

A chord which passes through the centre of the circle is

called adiameter. We denote the length of the diameter

byd.

Anarcis a continuous part of the circle. The length of

an arc is called itsarclength.

Every arc has a correspondingsector, which is the portion

of the circle subtended by the same angleμas the arc.

The formulae for the circumference and area of a circle both involve the number¼or “pi”.¼is an irrational

number, and ¼¼ 3 : 14 :

Circle

Area A=¼r^2

Circumference C=¼d

or C=2¼r

Sector

Arclength s=

¡ μ

360

¢

£ 2 ¼r

Area A=

¡ μ

360

¢

£¼r^2

D CIRCLES AND SECTORS [6.3, 6.5]

radius

lengthr

centre

diameter

lengthd

chord

r

q

arc

sector

r

d

q° r

s

24 m

10 m

13 m 15 m

11 Parallelogram ABCD has AB=10cm and diagonal DB=15cm. If the shortest distance from C to

line AB is 8 cm, find the shortest distance from A to DB.

12 Find the area of this trapezium:

10 a A kite has diagonals of length 16 cm and 10 cm. Find its area.

b Find the area of a kite with diagonals of lengthacm andbcm.

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_09\201IGCSE01_09.CDR Thursday, 2 October 2008 11:50:35 AM PETER