areas, shapes and perimeters
DESCRIPTION
Overview of Simple Areas and Perimeters.TRANSCRIPT
Areas, Shapes and Perimeters
How to recognise, measure and calculate
Common Shapes
• There are many types of shape including pentagons, dodecahedrons, rhomboids and trapeziums.
• All straight edged shapes can be split into triangles.• Compound shapes are irregular shapes made up of similar
shapes. By breaking these down into their component parts we can work out their dimensions.
• Being able to recognise a few basic shapes we can more readily break down more complex shapes into their component parts and so measure and calculate the correct dimensions.
Triangles
• Triangles are easily recognisable due to their three straight sides.• The internal angles of a triangle add up to a total of 180o.• Where all the sides of a triangle are of equal length the triangle is
know as an equilateral triangle.• Where any two of the sides are of equal length the triangle is known
as an isosceles triangle.
Squares
• The internal angles of a square add up to 360o, 90o at each corner.
• All the sides of a square are of equal length.
• A square can be split into two right angled, isosceles triangles.
• We use the total of number of one by one squares any shape would cover to define the area.
Circles
• Circles are shapes with no straight edges.• Any point on the curve of the circle is the same distance from its centre
as any other point on the curve.• Working out the dimensions of circles or segments involves using a
constant known as Pi (Π) and has an approximate value of 3.14.• Often when working with circles and segments people use radians to
measure the angles.
π x diameter = circumference
π x (radius)2 = area
Rectangles
• A rectangle is a four sided shape where the internal angle of each corner is 90o.
• The opposite sides of a rectangle are equal in length.• A rectangle may be split into two right angled triangles.• Rectangles are one of the most common types of shape and most
compound shapes can be split into rectangles of various sizes to easily calculate the dimensions.
Parallelograms
• A parallelogram is a four sided shape where the opposite sides run parallel to each other.
• The opposite sides of a parallelogram are of equal length.• If all the sides of a parallelogram are equal in length it is know as a
rhombus.• You can calculate the area of a parallelogram by cutting the end off
and using it to make a rectangle.
Trapezium
• A trapezium has two parallel sides.• By taking the average length of the parallel sides you can calculate
the area as though it were a rectangle.• A trapezium can be split into two right angled triangles and a
rectangle.• In the US the shape is referred to as a trapezoid.
Perimeter
• The perimeter is the length of the outside edge of any shape.
• For any shape by adding together the total length of all the shapes sides you will establish the perimeter.
• The perimeter of a circle is equal to the length of its only side also known as its circumference.
• The perimeter might also be referred to as the edge.
• When working out the size of a boundary you are calculating the perimeter.
Area
• The area of a shape is worked out by calculating the total number of 1 by 1 squares it covers.
• Partially covered squares are included in equal proportion to the amount of the square covered.
• Because of the method of calculating areas, multiplying two lengths together, the units they are measured in are squared units (e.g. metres [m] become metres squared [m2]).
• Area is used frequently in a large variety of roles, from landscaping to decorating, from construction to printing.
Examples
• Find the area and perimeter of the following shape.
4 m
4 m
Examples
• Find the area and perimeter of the following shape.
4 m
4 m
Area = 16 m2
Perimeter = 16 m
Examples
• Find the area and perimeter of the following shape.
3 m
6 m
Examples
• Find the area and perimeter of the following shape.
3 m
6 m
Area = 18 m2
Perimeter = 18 m
Examples
• Find the area and perimeter of the following shape.
2 m
2 m
4 m
4 m
Examples
• Find the area and perimeter of the following shape.
2 m
2 m
Area = 12 m2
Perimeter = 16 m
4 m
4 m
Basic Rules
• Perimeter = total length of all the sides added together.• Areas
– Square = Length of any side squared. (a2)– Rectangle = Length of one side times the length of an adjacent side. (a x b)– Triangle = Length of the base times the height all divided by 2. ((b x h) / 2)– Parallelogram = Length of the base times the height. (b x h)– Trapezium = Length of the parallel sides totalled together and divided by 2 with
the result multiplied by the height. (((a + b) / 2) x h)
• Circles– Perimeter = Circumference = π x Diameter– Area = π x Radius2
Questions• Calculate the Perimeter and Area of the following quadrilaterals:
5m6m
8m
8m
3m
6m
2m
6m
4m
12m
3m6m
Questions• Calculate the Perimeter and Area of the following quadrilaterals:
5m6m
8m
8m
3m
6m
2m
6m
4m
12m
3m
16m
24m
32m
18m
32m
16m36m2 6m
18m2
12m2
48m2
15m2
64m2
Questions• Work out the Perimeter and Area of the following triangles:
5m
3m
4m
6m
7m
6m
4m
6m
8m4m
5m 5m5m 3m
Questions• Work out the Perimeter and Area of the following triangles:
5m
3m
4m
6m
7m
6m
4m
6m
8m4m
5m 5m5m 3m 18m
6m2
16m
10m2
17m
12m212m
12m2
Questions• Work out the Perimeter and Area of the following compound shapes:
7m
9m
5m
3m
4m3m
2m
2m
2m
2m
2m2m
Questions• Work out the Perimeter and Area of the following compound shapes:
7m
9m
5m
3m
4m3m
2m
2m
2m
2m
2m2m
36m
45m2
24m
20m2
Questions• Calculate the Perimeter and Area of the following shapes:
7m2m
7m
2m
4m
4m
4m
4m
5m
4m4m
3m
6m
Assumeπ = 3.14
Questions• Calculate the Perimeter and Area of the following shapes:
7m2m
7m
2m
4m
4m
4m
4m
5m
4m4m
3m
6m
25.12m
50.24m2
18m
12m2
14m
9m2
20m
22m2
Assumeπ = 3.14