Source: Questions from Complete International Mathematics For Cambridge IGCSE - David Rayner, Jim Fenson

1. Find area of each shape.

2. A trapezium of area 140  sq cm has parallel sides 10 cm apart and one of these sides is 16 cm long.
    Find the length of the other parallel side.

3. A floor 5 m by 20 m is covered by square tiles of side 20 cm.
    How many tiles are needed.

 The number of tiles required cab be obtained by dividing the
 area of floor by the area of one tile
Step 1: Find area of floor.
Step 2: Find area of one tile
Step 3: Divide floor area by tile area.

4. A rectangular field, 400 m long, has an area of 6 hectares.
    Calculate the perimeter of the field.

 Step 1: Find breadth of the rectangular field.
Step 2: Calculate Perimeter

5.Find the length of a side of an equilateral triangle of area 10.2 sq m.


6. A regular hexagon is circumscribed by a circle of radius 3 cm with center O.

    a) What is angle EOD?
    b) Find the area of the triangle EOD and hence find area of hexagon ABCDEF.


7. The area of a regular pentagon is 600 sq cm. 
    Calculate the length of one side of the pentagon.


8. Discs of radius 4 cm are cut from a rectangular plastic sheet of length 84 cm and width 24 cm.
    a) How many complete discs can be cut out?
    b) the total area of the discs cut
    c) the area of the sheet wasted.


9. A circular pond of radius 6 m is surrounded by a path of width 1 m.  

    a) Find the area of the path
    b) The path is resurfaced with astroturf. 
        It is bought in packs each containing enough to cover an area of 7 sq m.
        How many packs are required?

 b)  Each astroturf pack covers an area = 7 sq m.

10. A golf ball of diameter 1.68 inches rolls a distance of 4 m in a straight line.
     How many times does the ball rotate completely?
     (1 inch = 2.54 cm)

Each time the ball rolls completely is one full circumference of the ball
Hence Step 1: Calculate circumference of the ball
Step 2: Divide it by the total distance rolled to see the number of complete rotations

11. A square is inscribed in a circle of radius 7 cm. Find:

     a) the area of the square
     b) the area shaded blue.

 b)Area of square subtracted from the area of circle will
give us the area of the four sectors.
This can be divided by 4 to give us the area of portion shaded blue.

12. The diagram shows a circle inside a rectangle.

     The pink shaded area is 84 sq cm. Find x.


13.The semi-circle and the isosceles triangle have the same base AB.

    They have the same area. Find the angle x.


14.The diameter of a circle is given as 10 cm, correct to the nearest cm. 
     a) the maximum possible circumference
     b) the minimum possible area of the circle consistent with this data.