Cambridge Additional Mathematics

Straight line graphs (Chapter 7) 185

b The length of AB=

p

(1¡¡4)^2 +(1¡6)^2 =

p

50 = 5

p

2 units

The length of DC=

p

(2¡¡7)^2 +(¡ 6 ¡3)^2 =

p

162 = 9

p

2 units

The length of AD=

p

(¡ 7 ¡¡4)^2 +(3¡6)^2 =

p

18 = 3

p

2 units

) the area of the trapezium=

μ

5

p

2+9

p

2

2

¶

£ 3

p

2

=7

p

2 £ 3

p

2

=42units^2

5 PQRS is a trapezium in which PQ is parallel to SR, and

PbSR=90±. Find:

a the coordinates of S

b the area of the trapezium.

6 ABC is a triangle in which AbBC=90±, and C lies on the

x-axis. Find:

a the coordinates of C

b the area of the triangle.

7 A trapezium ABCD has vertices A(3,0),B(¡ 2 ,¡5),C(¡ 4 ,1), and D. The side AD is parallel to

BC, and the side CD is perpendicular to BC. Find the area of the trapezium.

8 ABC is a triangle in which AbBC=90±, AC is parallel to

thex-axis, M is the midpoint of AB, and N is the midpoint

of BC.

a Find the coordinates of:

i B ii C iii N

b Show that MN is parallel to AC.

c Find the area of:

i trapezium AMNC ii triangle ABC.

Area of trapezium

μ

a+b

2

¶

= £h

a

h

b

S

R,(6 2)

Q,(2 5)

P,(-2 3)

y

x

O

A,(-3 10)

B,(3 6)

C

y

O x

A,(-3 -4)

B

N

C

M,(1 -2)

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_07\185CamAdd_07.cdr Monday, 6 January 2014 11:53:19 AM BRIAN