1. Finding the area of parallelograms and trapeziums

2. Area is 2-dimensional like a carpet or an area rug.
A parallelogram is a 4-sided shape formed by two pairs of parallel lines.
To find the area of a parallelogram, multiply the base by the height.

3. To find the area of a parallelogram, multiply the base by the height.
A = b . h
where b is the base, h is the height,
and . means multiply.

4. Example 1: Find the area of a parallelogram with a base of 12 centimetres and a height of 5 centimetres.
Solution: A = b.h
= (12 cm) · (5 cm)
= 60 cm2

5. Example 2: Find the area of a parallelogram with a base of 7 metres and a height of 10 metres
Solution: A = b.h
= (7 m) · (10 m)
= 70 m2

6. Area of a Trapezium
A trapezium is a quadrilateral that has only one pair of parallel sides.
Consider the area of the following trapezium.
                                                                                             

7. To calculate the area of a trapezium, divide it into a rectangle and two triangles as shown below.
                                                                                   

8. Area for a kite
Area = half the product of diagonals
A = ½ ab a b

9. Area of trapezium = area of triangle plus the area of the rectangle
Now, piece together the triangular ends so that the trapezium is divided into a triangle and rectangle. 
Area of trapezium = area of triangle plus the area of the rectangle
                                                                                       

10. Area of trapezium = area of triangle plus the area of the rectangle

11. The formula for the area of a trapezium is:
Area = height x average length of the two parallel sides
Area = h x a + b 2