8.64 Chapter 8
30. The coordinates of the four vertices of a trapezium are A(-4 , 0),
B(0 , 6), C(6 , 0) and D(0 , -9).
(a) Draw the trapezium ABCD in a rectangular coordinate plane.
(b) Find the area of trapezium ABCD.
31. (a) Draw a hexagon PQRSTU with vertices P(2 , 2), Q(0 , 2),
R(-1 , 0), S(-3 , -2), T(5 , -2) and U(3 , 0) in a rectangular
coordinate plane.
(b) Find the area of hexagon PQRSTU.
32. The figure shows a trapezium OEFG. H is the point of intersection
of EF and the y-axis.
(a) Write down the coordinates of H.
(b) Find the lengths of EF and OH.
(c) If the area of trapezium OEFG is 25 sq. units, find the value of x.
33. In the figure, PQRS is a parallelogram, where PS and QR are
horizontal lines. Its area is 144 sq. units and QR = 12 units.
(a) Find the coordinates of R.
(b) Find the value of a.
(c) Hence, find the coordinates of P.
34. In the figure, J(4a - 4 , -a), K(48 , 0), L(31 , 0),
M(3a + 3 , 3a + 3) and N(17 , 0) are vertices of hexagon OJKLMN.
The area of OJKLMN is 336 sq. units.
(a) Find the value of a.
(b) Is MJ a vertical line? Explain your answer.
35. A(4 , -3) and B(-7 , -3) are rotated clockwise about the origin O
through 270c to Al and Bl respectively.
(a) Find the coordinates of Al and Bl.
(b) Is it true that AB = AlBl? Explain your answer.
y
x
O G(x ,0)
F(4,- 5)
E(-3,-5) H
y
x
O
S(9,a)
Q(-6,-3)
P
R
y
x
O
N KL
M
J
Explain
Explain
3
3
3
3
3
4
18 sq. units
75 sq. units
(0 , -5)
(6 , -3)
7
Al(3 , 4), Bl(3 , -7)
3
(-3 , 9)
EF = 7 units, OH = 5 units
9
yes
yes