Areas of quadrilaterals

Calculating areas

1. Area of a rectangle All the angles in a rectangle are 90 o , so the area is given by: Area of a rectangle = length x breadth ( A = lb ) For example ; 12cm 7cm Here the length is 12cm and the width is 7cm so, Area = length x width = 12cm x 7cm = 84cm 2 Remember that: c m x cm = cm 2

2. Area of Square A square is some kind of a rectangle where the length is equal to the breadth. So, Area of a Square = length x length ( or breadth x breadth) To use a common term, Area of a Square = side x side ( A = s x s or A = s 2 ) For example ; Calculate the area of a square of side 8cm. 8cm Here each side is 8cm, so Area = side x side = 8cm x 8cm = 64cm 2 Remember that: c m x cm = cm 2

3. Area of a Parallelogram A parallelogram is a four sided figure with two opposite sides equal and parallel. Opposite angles are also equal. Its area is given by; Area of a parallelogram = b ase x h eight ( A = bh ) For example; Calculate the are of a parallelogram below; Base Height Area = base x height = 7cm x 3cm = 21cm 2 Note that we are using 3cm instead of 4cm because the height is always perpendicular to the base

4. Area of a Rhombus A rhombus is a special type of parallelogram in which all sides are equal. So we use the same formula; Area of a Rhombus = b ase x h eight ( A = bh ) For example; Calculate the are of a parallelogram below; Base Height Area = base x height = 5cm x 4cm = 20cm 2 Note that the height is 4cm not 5cm

5. Area of a Kite A kite is a four sided figure with two pairs of adjacent sides equal. It has two diagonals crossing at right angles. Only one of the diagonals is bisected, see the figure below; Using diagonals a and b in the diagram above, the area of kite is given by; Area of a Kite = x ab Example Calculate the area of a kite below Area = ½ x 6 x 13 = ½ x 78 = 39 In this example a = 3+3 and b = 4+9

6. Area of a Trapezium A trapezium is another four sided figure with only one pair of opposite sides parallel to each other as shown in the diagram below; Using diagonals a, b and h in the diagram above, the area of kite is given by; Area of a Trapezium = ( a+b )h Example Calculate the area of a kite below Area = ½ x (4+7)5 = ½ x 11 x 5 = 27.5