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2. AREA OF
PLANE
FIGURES
MATHEMATICS

3. AREA OF A RECTANGLE
Q.1 : Define area of rectangle
We can find the area of a rectangle by multiplying the length and
the breadth of the rectangle together.
length, l
breadth, b
Area of a rectangle
= length × breadth
= l x b
Area is measured in square units.
For example, we can use mm2, cm2, m2 or km2.
The 2 tells us that there are two dimensions, length and breadth.

4. RECTANGLE
The perimeter of a rectangle with length l and breadth b can be
written as:
l
b
Perimeter = 2l + 2b
or
Perimeter = 2 x (l + b)
The area of a rectangle is given as:
Area = l x b

5. AREA OF A RECTANGLE
8 cm
4 cm
Area of a rectangle = lw
= 8 cm × 4 cm
= 32 cm2

6. AREA OF SHAPES MADE FROM RECTANGLES
How can we find the area of this shape?
7 m
10 m
8 m
5 m
15 m
15 m
We can think of this shape as
being made up of two
rectangles.
Either like this …
… or like this.
Label the rectangles A and B.
A
B Area A = 10 × 7 = 70 m2
Area B = 5 × 15 = 75 m2
Total area = 70 + 75 = 145 m2

7. AREA OF SHAPES MADE FROM RECTANGLES
Area A = 5 × 7 = 35 m2
Area B = 5 × 15 = 75 m2
Total area = 35 + 75 = 110 m2
7 m
10 m
5 m
15 m
A
B

8. 6 cm
2 cm
2 cm
8 cm
12 cm
4 cm
4 cm
6 cm
2 cm
2 cm
8 cm
12 cm
4 cm
4 cm
24 cm2
8 cm2
8 cm2
Area = 24 + 8 + 8 = 40 cm2
2 cm
2 cm
16 cm2
12 cm2
12 cm2
Area = 16 + 12 + 12 = 40 cm2

9. AREA OF SHAPES MADE FROM RECTANGLES
How can we find the area of the shaded shape?
We can think of this shape
as being made up of one
rectangle with another
rectangle cut out of it.
7 cm
8 cm
3 cm
4 cm Label the rectangles A and B.
A
B
Area A = 7 × 8 = 56 cm2
Area B = 3 × 4 = 12 cm2
Total area = 56 – 12 = 44 cm2

10. AREA OF SHAPES MADE FROM RECTANGLES
A hotel is carpeting a function hall which has a wooden
dance floor within it. Calculate the area of carpet required.
This shape can be thought of as
made up of one rectangle cut out
of another rectangle.
9cm
11cm
4cm
6cm
Label the rectangles A and B.
A
B Area A = 9 × 11 = 99cm2
Area B = 4 × 6 = 24cm2
Total area = 99 – 24 = 75cm2

11. SQUARES
When the length and the width of a rectangle are equal we call it
a square. A square is just a special type of rectangle.
Perimeter = 4l
The area of a square is given as:
Area = l2
l
The perimeter of a square with length l is given as:

12. AREA OF A RIGHT-ANGLED TRIANGLE
We can use a formula to find the area of a right-angled
triangle:
base, b
height, h
Area of a triangle =
1
2
× base × height
=
1
2
bh

13. AREA OF A RIGHT-ANGLED TRIANGLE
What proportion of this rectangle has been shaded?
8 cm
4 cm
What is the shape of the shaded part?
What is the area of this right-angled triangle?
Area of the triangle = × 8 × 4 =
1
2
4 × 4 = 16 cm2

14. AREA OF A RIGHT-ANGLED TRIANGLE
Calculate the area of this right-angled triangle.
6 cm
8 cm
10 cm
To work out the area of
this triangle we only need
the length of the base
and the height.
We can ignore the third
length opposite the right
angle.
Area =
1
2
× base × height
= × 8 × 6
1
2
= 24 cm2

15. AREA OF A TRIANGLE
The area of any triangle can be found using the formula:
Area of a triangle = × base × perpendicular height
1
2
base
perpendicular height
Or using letter symbols:
Area of a triangle = bh
1
2

16. AREA OF A TRIANGLE
Any side of the triangle can be taken as the base, as long as the
height is perpendicular to it:
b
h
b
h b
h

17. AREA OF A TRIANGLE
What is the area of this triangle?
Area of a triangle = bh
1
2
7 cm
6 cm
=
1
2
× 7 × 6
= 21 cm2

18. AREA OF AN IRREGULAR SHAPES ON A PEGBOARD
E
D
C
B
A
We can divide the shape into
right-angled triangles and a
square.
Area A = ½ × 2 × 3 = 3 units2
Area B = ½ × 2 × 4 = 4 units2
Area C = ½ × 1 × 3 = 1.5 units2
Area D = ½ × 1 × 2 = 1 unit2
Area E = 1 unit2
Total shaded area = 10.5 units2
How can we find the area of this irregular
quadrilateral constructed on a pegboard?

19. AREA OF AN IRREGULAR SHAPES ON A PEGBOARD
Area A = ½ × 2 × 3 = 3 units2
A B
C D
Area B = ½ × 2 × 4 = 4 units2
Area C = ½ × 1 × 2 = 1 units2
Area D = ½ × 1 × 3 = 1.5 units2
Total shaded area = 9.5 units2
Area of irregular quadrilateral
= (20 – 9.5) units2
= 10.5 units2
How can we find the area of this irregular
quadrilateral constructed on a pegboard?

20. AREA OF A PARALLELOGRAM
Area of a parallelogram = base × perpendicular height
base
perpendicular
height
The area of any parallelogram can be found using the
formula:
Or using letter symbols:
Area of a parallelogram = bh

21. AREA OF A PARALLELOGRAM
What is the area of this parallelogram?
Area of a parallelogram = bh
12 cm
7 cm
= 7 × 12
= 84 cm2
8 cm
We can ignore
this length

22. AREA OF A PARALLELOGRAM
What is the area of this parallelogram?
Area of a parallelogram = bh
12 cm
7 cm
= 7 × 12
= 84 cm2
8 cm
We can ignore
this length

23. CUBES AND CUBOIDS
A cuboid is a 3-D shape with edges of different lengths. All of its
faces are rectangular or square.
Face
Edge Vertex
How many faces does a
cuboid have? 6
How many edges does a
cuboid have? 12
How many vertices does a
cuboid have? 8
A cube is a special type of cuboid with edges of equal length. All
of its faces are square.

24. LENGTH AROUND THE EDGES
To find the length around the edges of a cuboid of length l,
breadth b and height h we can use the formula:
Length around the edges = 4l + 4b + 4h
or
Length around the edges = 4(l + b + h)
To find the length around the edges of a cube of length l we can
use the formula:
Length around the edges = 12l

25. LENGTH AROUND THE EDGES
5 cm
4 cm
3 cm
Suppose we have a cuboid of length 5 cm, width 4 cm and
height 3 cm. What is the total length around the edges?
Imagine the cuboid as a hollow wire frame:
The cuboid has 12 edges.
4 edges are 5 cm long.
4 edges are 4 cm long.
4 edges are 3 cm long.
Total length around the edges = 4 × 5 + 4 × 4 + 4 × 3
= 20 + 16 + 12
Perimeter = 48 cm

26. SURFACE AREA OF A CUBOID
To find the surface area of a cuboid, we calculate the total area of
all of the faces.
A cuboid has 6 faces.
The top and the bottom of the
cuboid have the same area.

27. SURFACE AREA OF A CUBOID
To find the surface area of a cuboid, we calculate the total area of
all of the faces.
A cuboid has 6 faces.
The front and the back of the
cuboid have the same area.

28. SURFACE AREA OF A CUBOID
To find the surface area of a cuboid, we calculate the total area of
all of the faces.
A cuboid has 6 faces.
The left hand side and the right
hand side of the cuboid have the
same area.

29. FORMULA FOR THE SURFACE AREA OF A CUBOID
We can find the formula for the surface area of a cuboid as
follows.
Surface area of a cuboid =
h
l b
2 × lb Top and bottom
+ 2 × hb Front and back
+ 2 × lh Left and right side
Surface area of a cuboid = 2lb + 2hb + 2lh

30. SURFACE AREA OF A CUBOID
To find the surface area of a shape, we calculate the total area
of all of the faces.
So the total surface area =
7cm
8 cm 5 cm
2 × 40 cm2
+ 2 × 35 cm2
+ 2 × 56 cm2
Top and bottom
Front and back
Left and right side
= 80 + 70 + 112 = 262 cm2

31. SURFACE AREA OF A CUBOID
This cuboid is made from alternate purple and green
centimetre cubes.
What is its surface area?
Surface area
= 2 × 3 × 4 + 2 × 3 × 5 + 2 × 4 × 5
= 24 + 30 + 40
= 94 cm2
How much of the surface
area is green?
47 cm2

32. FORMULA FOR THE SURFACE AREA OF A CUBE
How can we find the surface area of a cube of length l?
l
All six faces of a cube have the same
area.
The area of each face is l × l = l2
Therefore,
Surface area of a cube = 6l2

33. SURFACE AREA OF A CUBE
Find the surface area of a cube of length 4 cm ?
l = 4 cm
Surface area of a cube = 6 x (l)2
= 6 x (4)2 = 6 x 4 x 4 = 96 cm3

34. USING NETS TO FIND SURFACE AREA
5 cm
6 cm
3 cm
6 cm
3 cm
3 cm
3 cm
It can be helpful to use the net of a 3-D shape to calculate its
surface area.
Here is the net of a 3 cm by 5 cm by 6 cm cuboid.
Write down the
area of each
face.
15 cm2 15 cm2
18 cm2
30 cm2 30 cm2
18 cm2
Then add the
areas together to
find the surface
area.
Surface Area = 126 cm2

35. USING NETS TO FIND SURFACE AREA
What is its surface area?
6 cm
5.2 cm
Area of each face = ½bh
= ½ × 6 × 5.2
= 15.6 cm2
Surface area = 4 × 15.6
= 62.4 cm2

36. Area of a trapezium
The area of any trapezium can be found using the formula:
Area of a trapezium = (sum of parallel sides) × height
1
2
Or using letter symbols:
Area of a trapezium = (a + b)h
1
2
perpendicular
height
a
b

37. Area of a trapezium
9 m
6 m
14 m
Area of a trapezium = (a + b)h
1
2
= (6 + 14) × 9
1
2
= × 20 × 9
1
2
= 90 m2
What is the area of this trapezium?

38. Area of a trapezium
What is the area of this trapezium?
Area of a trapezium = (a + b)h
1
2
= (8 + 3) × 12
1
2
= × 11 × 12
1
2
= 66 m2
8 m
3 m
12 m

39. Area problems
7 cm
10 cm
What is the area of the
yellow square?
We can work this out by subtracting
the area of the four blue triangles from
the area of the whole blue square.
If the height of each blue triangle is 7 cm, then the base is 3 cm.
Area of each blue triangle = ½ × 7 × 3
= ½ × 21
= 10.5 cm2
3 cm
This diagram shows a yellow square inside a blue square.

40. Area problems
7 cm
10 cm
We can work this out by subtracting
the area of the four blue triangles from
the area of the whole blue square.
There are four blue triangles so:
Area of four triangles = 4 × 10.5 = 42 cm2
Area of blue square = 10 × 10 = 100 cm2
Area of yellow square = 100 – 42 = 58 cm2
3 cm
This diagram shows a yellow square inside a blue square.
What is the area of the
yellow square?

41. Area formulae of 2-D shapes
You should know the following formulae:
b
h
Area of a triangle = bh
1
2
Area of a parallelogram = bh
Area of a trapezium = (a + b)h
1
2
b
h
a
h
b

42. Using units in formulae
Remember, when using formulae we must make sure that all
values are written in the same units.
For example, find the area of this trapezium.
76 cm
1.24 m
518 mm
Let’s write all the lengths in cm.
518 mm = 51.8 cm
1.24 m = 124 cm
Area of the trapezium = ½(76 + 124) × 51.8
= ½ × 200 × 51.8
= 5180 cm2
Don’t forget to
put the units at
the end.