Calculate the number of sides a regular polygon has if an interior angle is five times the size of an exterior angle.

In the diagram, XY and YZ are both tangents to the circle with center O.
a) Calculate $\angle \mathrm{OZX}$. b) Calculate the length XZ.

In the following diagram, O marks the centre of the circle. Calculate the value of x in each case.

The diagram dicussed before shows a scale model of a garage. Its width is 5cm, its length 10 cm and the height of its walls 6cm.
a) If the width of the real garage is $4 \mathrm{~m}$, calculate: i) the length of the real garage ii) the real height of the garage wall.b) If the apex of the roof of the real garage is $2 \mathrm{~m}$ above the top of the walls, use Pythagoras' theorem to find the real slant length $l$. c) What is the area of the roof section A on the model?

An equilateral triangle has an area of $25 \ cm^{2}$. If the lengths of its sides are reduced by 15%, calculate the area of the reduced triangle.

A cuboid has dimensions as shown in the earlier diagram : If the cuboid is enlarged by a scale factor of 2.5, calculate:
a) the total surface area of the original cuboid b) the total surface area of the enlarged cuboid c) the volume of the original cuboid d) the volume of the enlarged cuboid.

Define wat, batik, longhouse.

Consider a trapezium ABCD with AB=CD and BC parallel to AD. Given that AB = 12 cm, BC = 13 cm, and CD = 22 cm,

a. show that the trapezium has height 12 centimetres.

b. Hence, find the area of the trapezium.

c. Find the size of the angle C.

d. Calculate the length of the diagonal AC.

The triangle ADE shown has an area of 12 $\mathrm{cm}^2$.

a Calculate the area of triangle ABC.

b Calculate the length BC.

In the following diagram, O marks the centre of the circle. Calculate the value of x in each case.

In the trapezium calculate the lengths of the sides e and f.

In the given diagram, calculate the size of the labelled angles.

In the following question, some of the angles are given. Deduce, giving your reasons, the size of the other labelled angles.

What is the size of each exterior angle of a regular pentagon? Write your answer.