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# 9 perimeter, area volume

## by Skills for Life, Suffolk New college on Oct 26, 2010

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## 9 perimeter, area volumePresentation Transcript

• 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
• 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
• Perimeter
• The distance around a shape!
Shape 1 Shape 2 6cm 5cm 10cm 5cm 8cm
• Working out
• Shape 1 is a rectangle, what is its perimeter?
• Shape 2 is a Trapezium, what is its perimeter?
• Perimeter
• Not all sides are labelled – These need to be worked out!
20 cm 32 cm 15 cm 6 cm 5 cm 5 cm
• Working out
• What is the Perimeter of the shape on the previous Slide?
• Area
• Squared Units
We measure flat surfaces In square units so we must know how wide A shape is and how high = one square unit If Then this square has fifteen rows and Fifteen columns of unit squares So the area of the large square Is 15 x 15 = 225 units 2
• Area
• 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
• Volume
• Cubed units
• 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
• Circles
• What do we call the distance from the centre to the outside of a circle?
• Circles
• The Distance all the way across a circle is the
DIAMETER The diameter is double the radius
• 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
• 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!)
• 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 calculate The Circumference?
• 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
• Working out
• 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 calculate The Circumference? C= 2 r So we can now calculate the Circumference C= 2 x 3.14 x 10 = 62.8m
• 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 calculate The Area?
• 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
• Working out
• Calculating the Area of a Circle
• Let’s consider the circle below, and say that it has a Radius that measures 10metres
r A= 2 So Here Area= 3.14 x (10 x 10) A= 314m 2
• 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
• 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
• Example of A Composite Shape What in formation do you need?
• Working out
• Example of A Composite Shape We now know the area of the rectangle= 16x3 cm= 48 cm 3 cm 16 cm 2
• 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
• 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 cm 2 3 cm 8 cm
• Working out
• Example of A Composite Shape Area of Large = 0.5 x x (8x8) = 0.5x3.14 x 64 = 100.48cm 3 cm 8 cm 2 Area of small = 0.5 x x (3x3) = 0.5x3.14 x 9 = 14.13cm 2 Area shaded Blue= 100.48-14.13= 86.35 cm
• Example of A Composite Shape So we now have a total Area = 48+12+86.35= 146.35 cm 2
• Formulas for Area
• Area of Rectangle or Square
• = Length X Width
• Area of a Triangle = ½ X Base X Height