The perimeter of a quadrilateral is the length of the closed line around it, or in other words the sum of the four sides.

Work out the length of the perimeter of each of the quadrilaterals that you formed in the exercises on the previous page and write the answers in your notebook.

In the following window move points B, C and D of the quadrilateral to form these quadrilaterals and in each case check that the perimeter you obtain for each is the same as that in the diagram.

The area of a rectangle.

The area of a quadrilateral is the measurement of its surface area, or in other words the portion of area within the closed line or perimeter.

Units of area are defined as square metres (m2) in the decimal metric system. Its multiples are square decametres (Dm2), square hectometres (hm2) and square kilometres (km2) and its sub-multiples are square decimetres (dm2), square centimetres (cm2) and square milimetres (mm2). The choice of unit depends on the size of the quadrilateral we want to measure. 

In the following window there's a grid made up of 1cm2 squares that we're going to take as our basic unit of measurement. The base of the rectangle which is drawn (the horizontal side) is 5cm long and its height (the vertical side) is 3 cm long. To work out the area inside the rectangle we have to count how many little squares there are. There are 15 (5 x 3) so the size of the rectangle is 15cm2. In general,

the area of a rectangle of sides a and b is :

Work out the area of the following rectangles and write the answers in your notebook:

   1.      b= 5; a=4

   2.      b= 7.35; a=3.2

   3.      b= 16.45; a=8.7

   4.      b= 10; a=10

In the following window change a and b so that they have the same values as above and look at the area given in each case.

Note that the area of a square is l ², the length of its side being  l.

The area of a parallelogram.

In the following window form parallelograms whose base and height have the same value as in the exercise with rectangles on teh previous page. 

You can drag vertex B to change the angles of the parallelogram and you will notice that whatever the size of the angles are, the area is the same as that of the corresponding rectangle. This is because its base and height are always the same length as in the rectangle.

where D and d are the lengths of the diagonal sides of the rhombus.

Work out the area of the following rhombuses whose diagonal sides are:

    1.     7 and 10 units long.

    2.     5.5 and 7.8 units long.

    3.     21.8 and 20.9 units long.

Apply Pythagoras' theorem to work out the length of the sides of the rhombus.

In the following window apply the values given in the previous exercise to the two diagonal sides. Compare the results you get for the area and length of the sides of the rhombus with those given in the diagram.

Cut out two identical trapeziums of whatever shape you want with a pair of scissors. Turn one of them over and join it to the other by joining one of the none parallel sides as shown in the following diagram:

By doing this you will get a parallelogram whose base is the sum of the two parallel sides (called bases) of the trapezium: B and b where a is the height of the trapezium. The area of the trapezium is half that of the parallelogram. Therefore:

The area of a trapezium of bases "B" and "b" and height "a" is half of the base multiplied by the height.

Work out the area of the following trapeziums:

    1.     bases 7 & 10 units and height 8 units of length.

    2.     bases 5.5 & 7.8 units and height 10.1 units of length.

    3.     bases 21.8 & 20.9 units and height 9.5 units of length.

In each case form a trapezium with the measurements indicated above. Drag vertex B horizontally to make different-shaped trapeziums. As the size of the bases and height remain the same so does the area.