1. Area of Rectangles and Triangles
Mathematics
Area of Rectangles and Triangles

2. 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

3. 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

4. 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.

5. 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.

6. Example Let’s estimate the area of this shape. 1 2 3
First the grid of centimetre squares.
Count all full or over ½ squares.
Our total estimate is: 30cm²
You would be marked as correct if your estimate was between 27-32cm²

7. 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!

8. Example 1: Counting Squares
This rectangle is 3cm wide and 4cm long
The area units are cm²
There are 12 squares inside the rectangle
Its area is 12cm²

9. Example 2: Area Formula 4cm 3cm The formula for
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
4cm
3cm

10. Quick Practice Find the area (and units) of each of these shapes: 3cm

11. Quick Practice - Answers
Remember: Area of a Rectangle = Length × Width
3cm
8cm
Area = 8cm × 3cm = 24cm²
2.4m
50cm 9m
Area = 2.4m × 0.5m = 1.2m² OR
Area = 240cm × 50cm = 12000cm²
Area = 9m × 9m = 81m²

12. 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

13. 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:
Save and complete the worksheet called: AreaR-S1.xlsx
Now continue working through this powerpoint

14. 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

15. Quick Practice Find the area (and units) of each of these triangles:
10m
15m 8m
20mm
12mm
16mm
12cm
5cm
13cm

16. Quick Practice Remember: Area of a Triangle = ½ of Base × Perp. Height
20mm
12mm
16mm
12cm
5cm
13cm
12cm
5cm
13cm
Area = ½ of 10 × 8
= ½ of 80 = 40m²
Area = ½ of 12 × 16
= ½ of 192 = 96mm²
Area = ½ of 5 × 12
= ½ of 60 = 30cm²

17. 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:
Save and complete the worksheet called: AreaT-S1.xlsx
Now move on to the PAV-2b powerpoint