Area and Perimeter

First things first, technically speaking…..

What is perimeter?

What is area?‘The perimeter is the length of a closed

curve. The curve may be a smooth curve (e.g. an ellipse or a circle), or a broken curve (e.g. a

polygon).’Dictionary of Mathematics, Penguin

2003

‘Area is a measure of surface.’

Dictionary of Mathematics, Penguin 2003

( Or, the length of all a 2D shape’s edges added together)

( Or, the amount of surface the 2D shape covers. It’s measured in square units)

… and why do we need to know about it?

Working out how much you fencing you need to go round the garden.

Making sure the grounds man gets the lines of the rugby pitch (or any other sports pitch…) the right length.

Calculate how many tins of paint it will take to paint my bedroom the colour of a Mojito!

To check I’ll still have room to walk around

my king-size bed once it’s in my room!

Finding the right size cake tin for baking brilliant

brownies!

Checking your knitting is the right dimensions so your woolly jumper fits just right.

Perimeter and Area in disguise…

Spaghetti and Meatballs for All!: A Mathematical Story, Marilyn Burns, (Scholastic Bookshelf: Math Skills) 2008

Potential for misconceptions!!

Calculating perimeter by counting squares around shapes.

Perimeter of the green rectangle is 4+2+4+2 = 12, not 16, which it would work out as if the surrounding squares were counted.

2 2

4

4 This story is based on seating for a party, and sneakily discourages counting corner squares when counting perimeter because it’d be quite a squash with people sat on the corners too…

Building a conceptual understanding…

However the subject is broached, from the EYFS through KS1, pupils develop an understanding of shape, calculating and measuring in standard and non-standard units. These skills all come together under this topic, so pupils (and you, hopefully…) should be able to use what they know and apply it to calculating perimeters and areas.

Start with the basics… rectangles!

=

3 rows of 6 = 3 x 6 = 18 square units

Perimeter: 3 + 3 + 6 + 6 = 18 unitsArea:

6

3

RectanglesThis idea of breaking shapes up into individual units is something most pupils will have come across before, even if they aren’t necessarily aware of it…

=3x2 6 4x2 8

=

=4x1 4

=42x2

=2x1 2 3

=3x11x1 = 1

RectanglesThis idea of breaking shapes up into individual units is something most pupils will have come across before, even if they aren’t necessarily aware of it…

=3x2 6 4x2 8

=

=4x1 4

=42x2

=2x1 2 3

=3x11x1 = 1

Rectilinear shapes

l

Parallelograms

Parallelograms are also a special type of rectangle. They have 2 pairs of equal parallel sides, and it follows that...

Perimeter = l + l + s + s

Area = Length (l) x Vertical height (v)

l

v s

Squares

Squares are a special case of rectangles. They have 4 equal sides, so it follows that...

Perimeter = s + s + s + s = 4s

Area = s x s = s²

s

s

Rectilinear ShapesTrapeziums

Trapeziums are another a special type of rectangle. They have 1 pair of parallel sides, and it follows that...

Perimeter = a + b + c + d

Area = Vertical height (v) x ½(a + b)

v

a

b

c d

This knowledge about triangles can be applied to kites as well.

Diagonal 1

(d1)

Diagonal 2

(d2)

Area of kite = ½ d1 d2

a a

b b

Perimeter of kite = 2a + 2b

Kite