AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)


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1 AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square or a rectangle which is drawn on squared background e.g calculate the area of the following rectangle: The easiest way to do this is to count the squares inside the shape. As there are 18 squares inside this shape its area is 18 units 2 1
2 As you get used to doing this you will eventually spot that there is a quicker way to calculate the area of a square or a rectangle than counting squares Rather than spend a long time counting all the squares in the above rectangle, you can see that we have '7 rows of 11 squares' If we calculate 7 x 11 then this tells us that there are 77 squares This means that the area of this rectangle is 77units 2 2
3 Sometimes you have to calculate the area of shapes by counting squares and parts of squares. You need to be very careful to make sure that you count all the part squares accurately! e.g calculate the area of the following shape: There are 9 whole squares (red dots) but there are also 4 half squares (blue dots). four halves make 2 whole squares So the area of this shape is = 11units 2 3
4 The next step is to calculate the area of simple shapes that are not drawn on square background. To do this we need to use certain formulas depending on the shape Remember: AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 We need to be able to calculate the area of the following shapes: 1: The square Area of a square = width x height e.g calculate the area of the following square, To calculate the area we need to use the above formula 7cm area of a square = width x height As this is a square we should know that all sides are the same length so... area = 7cm x 7cm = 49cm 2 4
5 2: The Rectangle This is very similar to the square, in fact, it uses the same formula to calculate the area! area of a rectangle = width x height (units 2 ) e.g calculate the area of the following rectangle, 5m use the formula for a rectangle: 12m area = width x height we can see from the diagram that: width = 12m height = 5m so... area = 12m x 5m = 60m 2 5
6 3: The Triangle To find the area of a triangle we use the following formula: area of a triangle = width x height 2 which can also be written as area of a triangle = (width x height) 2 Dont forget your units units 2 e.g calculate the area of the following triangle, we need to use the formula 6cm area of a triangle = width x height 2 11cm From the diagram we can see that: width = 11cm and height = 6cm so... area = 6 x 11 = = 33cm 2 6
7 Once you have grasped how to calculate the area of basic shapes you can move on to some more shapes. The first shape would be a parallelogram To calculate the area of a parallelogram we use width x height e.g calculate the area of: 15m 6m 7m using the above formula we can see that width = 15m height = 6m (Note: we do NOT need the 7m height is NOT the length of a slanty side Height is always measured perpendicular (90 0 ) to the ground!) So area = 15 x 6 = 90m 2 dont forget your unit! 7
8 To calculate the area of a trapezium we use the following formula: Area = 1 ( a + b ) x h 2 Where h is the height (ALWAYS perpendicular NOT the length of one of the slanty sides of the trapezium) a and b are the lengths of the parallel sides. e.g Calculate the area of the following: 12cm using the above formula we can see that: h = 5, a = 12, b = 22 So we can put these numbers into the formula to work it out Area = 1 ( ) x 5 2 = 1 x 34 x 5 2 = 17 x 5 = 85cm 2 Dont forget your units 22cm 5cm 8
9 Next we move on to calculating the area of compound shapes A compound shape is what you get when you stick TWO OR MORE simple shapes together. e.g calculate the area of: Split this compound shape into its simpe shapes. Call them A and B. 17cm 8cm A? 12cm The long vertical edge on the left is 17cm. There is a 5cm vertical edge on the right. To figure out the height of A we calculate 5 +? = 17 B 15cm 5cm so we do 17 5 = 12 Work out the area of A and B seperately: A is a rectangle: area = width x height = 8cm x 12cm = 96cm 2 area of B = width x height = 15cm x 5cm = 75cm 2 Area of the whole shape = = 171cm 2 9
10 The next step is to be able to calculate the area of a circle. In order to do this you will need to be aware of some of the key parts and key words associated with circles Circumference: The length around a circle Radius (r): The distance between the centre of a circle and its circumference r Diameter (d): A straight line from one side of a circle to the other, passing through the middle d From the above diagrams you can see that the radius is half the length of the diameter (or the diameter is double the length of the radius) 10
11 Next we move on to calculating the area of a circle REMEMBER: π = 3.14 (pi) To calculate the area of a circle you use the following formula: Area = πr 2 (r is the radius) Calculate the area of: 10cm Area = πr 2 From the diagram we can see that the diameter is 10cm so the radius is HALF OF THIS: r = 5cm So, using the formula, Area = πr 2 becomes Area = 3.14 x 5 2 Square the radius FIRST and then multiply it by 3.14 = 3.14 x 25 = 78.5cm 2 11
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