Transcript MATHEMATICS Area of Rectangles and Triangles Lesson Objectives • The aim of this powerpoint is to help you… • understand what is meant by.

MATHEMATICS
Area of Rectangles and Triangles
Lesson Objectives
• The aim of this powerpoint is to help
you…
• understand what is meant by ‘area’
• estimate the area of any shape
• calculate the area of rectangles
• calculate the area of triangles
Area
• Area is the amount inside a 2D shape.
• You could count the ‘squares’ inside
OR
• Calculate it by multiplying 2 (perpendicular) distances
together
• REMEMBER:
2 distances added together just make a bigger distance
2 areas added together just make a bigger area
Units of Area
• Area is measured in ‘square’ units.
• Its metric units can be square millimetres (mm²), square
centimetres (cm²), square metres (m²) or square
kilometres (km²).
• Other metric units are ares and hectares.
• Its imperial units can be square inches, square feet,
square yards or square miles.
• Other imperial units are acres.
Estimating the area
• You can find or estimate an area by counting the number
of squares inside the shape.
• Put a grid of squares over the shape.
• Count all the squares of the grid that are at least ½
squares within the shape.
• Do NOT count any squares that are less than ½ squares
within the shape.
• Your total count is your estimated area.
Example
• Let’s estimate the area of this shape.
1 2 3
4 5 6 7
• First the grid of centimetre squares.
• Count all full or over ½ squares.
9 10 11 12 13
14 15 16 17 18 19
20 21 22 23 24
• Our total estimate is: 30cm²
25 26 27
28 29 30
• You would be marked as correct if
your estimate was between 27-32cm²
8
Area of a Rectangle (or Square)
• Remember…
• You can find the area by counting the number of squares
inside the shape
OR
• You can calculate the area by multiplying 2 perpendicular
distances together, in the case of a rectangle, these 2
distances would be its length and width.
• REMEMBER: To square something means to multiply it
by itself so distances MUST have the same type of units
before you multiply them together!
Example 1: Counting Squares
• This rectangle is 3cm wide
and 4cm long
• The area units are cm²
1
2
3
4
• There are 12 squares
5
6
7
8
9
10
11
12
inside the rectangle
• Its area is 12cm²
Example 2: Area Formula
• The formula for
4cm
the area of a rectangle is:
length × width, i.e. A = lw
• Here the length is 4cm and
the width is 3cm
• Area = 4cm × 3cm
• Its area is 12cm²
3cm
Quick Practice
• Find the area (and units) of each of these shapes:
3cm
8cm
2.4m
9m
50cm
Quick Practice - Answers
• Remember: Area of a Rectangle = Length × Width
3cm
Area = 8cm × 3cm = 24cm²
8cm
2.4m
9m
Area = 9m × 9m = 81m²
50cm
Area = 2.4m × 0.5m = 1.2m²
OR
Area = 240cm × 50cm = 12000cm²
Finding a Side given the Area
• The formula for the area of a rectangle is:
area = length × width
• If we already know the area, we can find the length or the
width by dividing the area by the known side:
width = area ÷ length
• If the shape is a square then we know the same value
was multiplied by itself (i.e. squared) to get the area so in
this case:
side length = area
What next?
• Print out the notes called PAV2a-Area. Read through
them and make sure you answer any questions on
estimating areas or areas of rectangles.
• Work through the MyMaths lesson and then its online
homework called Area of Rectangles found at:
• http://app.mymaths.co.uk/266-resource/area-of-rectangles
• http://app.mymaths.co.uk/266-homework/area-of-rectangles
• Save and complete the worksheet called: AreaR-S1.xlsx
• Now continue working through this powerpoint
Area of Triangles
• Look carefully at this triangle
• The length of the rectangle forms the base of the triangle
• The width of the rectangle forms the (perpendicular) height of the triangle
• The triangle has half the area of the rectangle.
• Area of rectangle =
length × width
• Area of triangle = ½ of base × p.height
• Formula: A = ½bh
Quick Practice
• Find the area (and units) of each of these triangles:
15m
20mm
16mm
10m
12mm
12cm
5cm
13cm
8m
Quick Practice
• Remember: Area of a Triangle = ½ of Base × Perp. Height
15m
20mm
16mm
8m
13cm
12cm
10m
12mm
12cm
5cm
5cm
Area = ½ of 10 × 8
= ½ of 80 = 40m²
Area = ½ of 5 × 12
Area = ½ of 12 × 16
= 13cm
½ of 60 = 30cm²
= ½ of 192 = 96mm²
What next?
• Continue reading through the PAV2a-Area notes and
make sure you answer any questions on areas of
triangles.
• Work through the MyMaths lesson and then its online
homework called Area of Triangles found at:
• http://app.mymaths.co.uk/268-resource/area-of-a-triangle
• http://app.mymaths.co.uk/268-homework/area-of-a-triangle
• Save and complete the worksheet called: AreaT-S1.xlsx
• Now move on to the PAV-2b powerpoint