Mr Barton’s Maths Notes Shape and Space 5. Area www.mrbartonmaths.com

5. Area A Quick Word about Area The Importance of Perpendicular Height Working out the areas of shapes is easy… so long as you remember the formulas! Sometimes you will be given them in exams, but more often they need to be fixed in your head! NEVER FORGET every time you work out an area, give your answer as SQUARED UNITS e.g. m2, cm2, km2, mm2 etc The Importance of Perpendicular Height As you will see, most of the formulas for area involve multiplying the base of the shape by it’s height… but it’s not just any old height! The height must be perpendicular to the base! What? All that means is that the height you measure must be at right angles (900) to the base So… if the base is horizontal (flat), then the height you want is vertical (straight up), not any slanted height that they may give you in the question to try and trip you up! rubbish Perpendicular height base rubbish base Perpendicular height

1. Rectangle 2. Triangle Example Example Area = h h b Area = b Area = What to do: Multiply the base by the height! What to do: Multiply the base by the (perpendicular) height and remember to divide your answer by 2! Example Example 3 cm Area = Area = = 60m2 15 m 9 cm = 27cm2 12 m 10 m

3. Parallelogram 4. Trapezium Example Example q h h Area = b p Area = What to do: Add together the lengths of your two parallel sides and divide the answer by 2. This gives you the average length of your base. Then multiply this by the vertical height! What to do: Multiply the base by the perpendicular height… definitely not the slanted height! Example Example Area = 5 mm 10 mm 12 mm 4.2 cm = 28cm2 2.8 cm Area = = 50mm2 8 cm

5. Kite 6. Circle Example Example r h Area = b Area = Area = Area = What to do: Find the radius of your circle (if you are given the diameter, just halve it!). Square the radius, and multiply your answer by pi! Area = What to do: The base and height in a kite are just the two diagonals from point to point… so multiply them together! Example Diameter = 12.6 m Example Radius = 6.3 m 12.6 m Area = Area = 2.5 m = 10m2 4 m = 124.7 m2 (1dp)

Compound Area Area = = 77mm2 Area = Total Area Area = 77 + 162 Sometimes you are given quite complicated shapes and asked to work out the area. The technique here is to split them up into some of the 6 shapes you know how to work out the area of and just add together your answers! Try to be as clear as you can in your working to keep Mr Examiner happy! I have chosen to split this shape up into a rectangle and a trapezium. It is also possible to split it up into rectangles and triangles. It is completely up to you! 1 2 1 Rectangle Area = Area = = 77mm2 2 Trapezium Total Area Area = 77 + 162 = 239 mm2 Area = = 162mm2

Surface Area 6 cm Area = 10 cm 2 cm 8 cm Area = = 24cm2 I think of surface area as the exact amount of wrapping paper you would need to wrap up a 3D shape. People get themselves into a right muddle with surface area questions, mostly because they do not set them out properly and they end up forgetting sides or counting some twice! All you need to do is think about what flat 2D shape is on each side of your 3D object, work out its area, and tick off that side! It’s just like compound area, only it gets you loads more marks! Okay, so once again I am going to number each side, decide what shape it is, work out it’s area, and then move onto the next! 5 3 2 1 Triangle 6 cm Area = 10 cm 1 2 cm 8 cm Area = 4 = 24cm2

Area = Area = = 20cm2 Area = = 12cm2 Area = Area = Area = 24cm2 Area = 3 2 Rectangle Rectangle Area = Area = = 20cm2 Area = = 12cm2 Area = 4 5 Triangle Rectangle 1 Exact same shape as Area = Area = 24cm2 Area = = 16cm2 Total Area 24 + 20 + 12 + 16 + 24 = 96 cm2

Good luck with your revision!