9 perimeter, area volume
TRANSCRIPT
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Ra
Measuring Shape and Space
This powerpoint is intended to be read in stages at the reader’s own pace.The main emphasis is to help adults understand
Perimeter, Area & Volume
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Units of Measurement
When we measure distances we use whole metres or parts of metres (centimetres or millimetres)
Some people might use yards or parts of yards (feet and inches)
We will concentrate on Metric units
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Perimeter
The distance around a shape!
Shape 1Shape 2
6cm
5c m
10cm
5cm
8cm
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Working out
Shape 1 is a rectangle, what is its perimeter?
Shape 2 is a Trapezium, what is its perimeter?
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Perimeter
Not all sides are labelled – These need to be worked out!
20 cm
32 cm
15
cm
6 cm
5 cm
5 cm
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Working out
What is the Perimeter of the shape on the previous Slide?
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Area
Squared Units We measure flat surfacesIn square units so we must know how wideA shape is and how high
= one square unitIf
Then this square has fifteen rows and Fifteen columns of unit squares
So the area of the large squareIs 15 x 15 = 225 units 2
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Area
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Working out
2
2
2
2
= 1 x 1 = 1 unit
= 2 x 2 = 4 unit
= 3 x 3 = 9 unit
= 4 x 4 = 16unit
2
2
2
2
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Volume
Cubed units
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Working out
On the previous slide we could fit three and a half unit cubes horizontally, we could fit three and a half vertically and we could fit three and a half from front to back. So we have measured in three directions (Dimensions). If we now multiply these dimensions together we get 3.5x3.5x3.5= 42.875 units
3
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Circles
What do we call the distance from the centre to the outside of a circle?
RADIUS
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Circles
The Distance all the way across a circle is the
DIAMETERThe diameter is double the radius
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Circumference
• The Circumference is the distance all the way round the outside of a circle.
• This is another name for the Perimeter of a Circle
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Circumference
• The Circumference is the distance all the way round the outside of a circle.
• A larger Circle will have a larger Circumference (So the bigger the Radius; the bigger the Circumference!)
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Calculating the Circumference
Let’s consider the circle below, and say that it has a Radius that measures 10metres
RADIUS Do you Know a Formula that we can use to calculateThe Circumference?
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Formulas for Circumference
• Circumference= 2 x x Radius
• Or C= 2 r•Or C= d • (Because 2r= diameter=d)
• is a special number for Circles= 3.14
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Working out
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Calculating the Circumference
Let’s consider the circle below, and say that it has a Radius that measures 10metres
Do you Know a Formula that we can use to calculateThe Circumference?
C= 2 rSo we can now calculate the Circumference
C= 2 x 3.14 x 10 = 62.8m
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Calculating the Area of a Circle
Let’s consider the circle below, and say that it has a Radius that measures 10metres
RADIUS
The Area here is the flat surface coloured blue. Do you know a formula that we can use to calculateThe Area?
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Formula for the Area of a Circle
• Area = x Radius squared
• Or A= r Remember to do r x r first then x
is a special number for Circles= 3.14
2
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Working out
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Calculating the Area of a Circle
Let’s consider the circle below, and say that it has a Radius that measures 10metres
rA=2
So Here Area= 3.14 x (10 x 10)
A= 314m2
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Area of a circle
• Now you practice with these circles
1
2
3
Area when diameter is 30 cm
Circumference of a circle radius = 35 metres
Area when diameter is 20 inches
You can use a calculator if you like! Or say = 3
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Composite shapes
• A composite shape is one that is constructed from two or more different shapes
• These different shapes could be a combination of Rectangles, Circles, Squares, or Triangles.
• All flat shapes will have a perimeter and some area
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Example of A Composite Shape
What in formation do you need?
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Working out
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Example of A Composite Shape
We now know the area of the rectangle= 16x3 cm= 48 cm
3 cm
16 cm
2
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Example of A Composite Shape
We can now see the two triangles are the same size so their combined area is the same as a rectangle 3cm x4cm= 12cm
4 cm
4 cm
2
3 cm
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Example of A Composite Shape
Let’s calculate the area of the large half Circle then take away the area of the small half circle
So far our Area running total is 48+ 12 cm2
3 cm8 cm
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Working out
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Example of A Composite Shape
Area of Large = 0.5 x x (8x8) = 0.5x3.14 x 64 = 100.48cm
3 cm8 cm
2
Area of small = 0.5 x x (3x3) = 0.5x3.14 x 9 = 14.13cm
2Area shaded Blue= 100.48-14.13= 86.35 cm
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Example of A Composite Shape
So we now have a total Area = 48+12+86.35= 146.35 cm
2
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Formulas for Area
Area of Rectangle or Square= Length X Width
Area of a Triangle = ½ X Base X Height