Contents:
Area: Square, Rectangle, Triangle, Circle, Parallelogram, Trapezium.
Rectangles: square and rectangle, area and perimeter.
The area of a square or rectangle
is the length multiplied the width (square can be measured as the length squared).
The perimeter of a square is the length multiplied by four, for a rectangle
the perimeter is twice the length plus twice the width.
Example: Find area and perimeter of a rectangle length: 4mm, width: 3mm.
Answer: Area = length x width = 12mm
. Perimeter = 2 x length + 2 x width = 14mm.
Triangles: acute triangle, and obtuse triangle; areas.
The area of a triangle can be calculated
in the same way as the rectangle; the height multiplied by the
base or width. However it is seen from the diagram that a triangle
only takes up half of the space of a rectangle (the yellow area).
The areas outside the triangle fit exactly inside. Therefore the
area = height x base
2. This
principle is also used for the obtuse triangle where the formula
is also height x base2.
Example: Find area of triangle base: 6mm, height: 5mm.
Answer: Area = 1/2 base x height = 15mm.
Circles: area and circumference.
pi = 3
14159 and known by the symbol 
.
The area of a circle is the square of the radius multiplied
by pi. radius. The perimeter, known as the 'circumference'
is calculated by 2 x radius (or diameter) x pi. The 'diameter' is a line from
one edge through the centre to the opposite edge.
Example: Find the area and circumference of a circle of radius: 5mm.
Answer: Area = 5= 3 1416 x 25 = 78 54mm.
Circumference = diameter x = 31416 x 10 = 31 42mm.
The area of a parallelogram is the height measured perpendicular
from the base multiplied by the width. The triangle 'a' in the diagram has exactly
the same area and can be exchanged to form a rectangle.
Example: Find the area of a parallelogram height: 4mm, width: 6mm.
Answer: Straighten up to rectangle shape, area = height
x width = 4 x 6 = 24mm.
The area of a trapezium is calculated similar
to the rectangle. First the two parrallel sides have to be identified.
The width is the average of the two lengths. The height is measured
similar to the parallelogram, perpendicular from the base.
Example: Find the area of a trapezium
with height 3mm, top width 5mm and bottom width 8mm.
Answer: Average width x height = (5+8)2
x 3 = 195mm.
Exercise in calculating areas:
