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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 1Shape 2

6cm

5c m

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 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

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?

RADIUS

Circles

The Distance all the way across a circle is the

DIAMETERThe 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 calculateThe 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 calculateThe Circumference?

C= 2 rSo 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 calculateThe 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

rA=2

So Here Area= 3.14 x (10 x 10)

A= 314m2

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 cm2

3 cm8 cm

Working out

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

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