 Topic Area and volumes of plane figures

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

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

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

Previous knowledge Square: side x side Rectangle : length x breadth
Triangle : ½ base x height or altitude Circle ∏r2 where r is the radius

Area of some special figures
Trapezium A trapezium has one pair of opposite side parallel A B AB is parallel to BD h C D Area=1/2h(sum of parallel sides)

Area of regular hexagon
We can find of hexagon in different ways

method1 This hexagon can be divided into two trapezium

Method 2 The hexagon is divided into two triangles and one rectangle

Surface area of a cylinder
Let us roll a rectangular sheet of paper 2 ∏r h

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

Volume : it s the space occupied by an object:
Volume of a cuboid= lx b x h Volume of a cylinder = ∏r2 h

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.

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.

Assignment Find the area of the given figures
4cm A regular hexagon having side 5cm 11cm

DC =11cm 3.5cm D C 2.5cm

Find the area of the each green region separately
20cm 16 28cm 24cm