MATHEMATICSArea 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’ insideOR

• 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.

• 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

1 2 3

4 5 6 7 8

9 10 11 12 13

14 15 16 17 18 19

20 21 22 23 24

25 26 27

28 29 30

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

• There are 12 squares inside the rectangle

• Its area is 12cm²

1 2 3 4

5 6 7 8

9 10 11 12

Example 2: Area Formula

• 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

Quick Practice

• Find the area (and units) of each of these shapes:

3cm

8cm

2.4m

50cm9m

Quick Practice - Answers

• Remember: Area of a Rectangle = Length × Width

3cm

8cm

2.4m

50cm9m

Area = 8cm × 3cm = 24cm²

Area = 9m × 9m = 81m²

Area = 2.4m × 0.5m = 1.2m²OR

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:

20mm

12mm

16mm

12cm5cm

13cm

10m

15m8m

Quick Practice

• Remember: Area of a Triangle = ½ of Base × Perp. Height

20mm

12mm

16mm

12cm5cm

13cm

10m

15m8m

Area = ½ of 12 × 16 = ½ of 192 = 96mm²

12cm

5cm

13cm

Area = ½ of 5 × 12 = ½ of 60 = 30cm²

Area = ½ of 10 × 8 = ½ of 80 = 40m²

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