Area and volumes of plane figures

1

• Topic
• Area and volumes of plane figures
• Area and volumes of solid figures

2
Learning outcomes

• Students will be able to understand the method of
  finding areas of figures like
• Trapezium
• Regular pentagon
• Cube
• cylinder

3

• They will be able to find the volume and surface
  area of
• Cuboids/cube
• Cylinder
• Apply the concepts in daily life mathematical
  problems.

4
Previous knowledge

• Square side x side
• Rectangle length x breadth
• Triangle ½ base x height or altitude
• Circle ?r2 where r is the radius

5
Area of some special figures

• Trapezium
• A trapezium has one pair of opposite side parallel

B
A
AB is parallel to BD
h
D
C
Area1/2h(sum of parallel sides)
6
Area of regular hexagon

• We can find of hexagon in different ways

7
method1

• This hexagon can be divided into two trapezium

8
Method 2
The hexagon is divided into two triangles and
one rectangle
9
Surface area of a cylinder

• Let us roll a rectangular sheet of paper

2 ?r
h
10

• We see that the length of the sheet will be the
  circumference of the circle
• And the height of the cylinder is the breadth of
  the sheet.
• Area of the sheet l x b which is same as
• Area of the cylinder 2 ?r x h

11

• Volume it s the space occupied by an object
• Volume of a cuboid lx b x h
• Volume of a cylinder ?r2 h

12

• The unit of measurement of area is square units e
  g cm2 m2 etc
• The unit of measurement of volume is cubic
  units e g cm3 m3 or if we are measuring liquids
  it will be ml litres.

13

• What is the difference between capacity and
  volume?
• What is the relation between the units cm3 and
  ml
• A rectangular sheet 11cm x 4 cm is folded to
  make a cylinder of height 4cm .Find the volume of
  the cylinder so formed.

14
Assignment

• Find the area of the given figures

A regular hexagon having side 5cm
4cm
11cm
15
DC 11cm
3.5cm
D
C
2.5cm
16
Find the area of the each green region separately
20cm
16
28cm
24cm