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Area and Perimeter

Area and Perimeter. First things first, technically speaking…. What is perimeter?. ‘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.

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Area and Perimeter

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  1. Area and Perimeter

  2. First things first, technically speaking….. What is perimeter? ‘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 amount of surface the 2D shape covers. It’s measured in square units) ( Or, the length of all a 2D shape’s edges added together) What is area?

  3. … and why do we need to know about it? Calculate how many tins of paint it will take to paint my bedroom the colour of a Mojito! Working out how much you fencing you need to go round the garden. Checking your knitting is the right dimensions so your woolly jumper fits just right. To check I’ll still have room to walk around my king-size bed once it’s in my room! Making sure the grounds man gets the lines of the rugby pitch (or any other sports pitch…) the right length. Finding the right size cake tin for baking brilliant brownies!

  4. Perimeter and Area in disguise… Potential for misconceptions!! Calculating perimeter by counting squares around shapes. 4 2 2 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… 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. Spaghetti and Meatballs for All!: A Mathematical Story, Marilyn Burns, (Scholastic Bookshelf: Math Skills) 2008

  5. 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 6 Perimeter: 3 + 3 + 6 + 6 = 18 units Area: 3 rows of 6 = 3 x 6 = 18 square units

  6. = = 1x1 = 1 3x1 2x1 2 3 = = 4x1 4 2x2 4 = = 4x2 8 3x2 6 Rectangles This 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…

  7. = = 1x1 = 1 3x1 2x1 2 3 = = 4x1 4 2x2 4 = = 4x2 8 3x2 6 Rectangles This 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…

  8. 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 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) v s Rectilinear shapes l

  9. a v c d b Rectilinear Shapes Trapeziums 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)

  10. Kite This knowledge about triangles can be applied to kites as well. a a Perimeter of kite = 2a + 2b Diagonal 1 (d1) Area of kite = ½ d1 d2 b b Diagonal 2 (d2)

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