Surface Area of a Pyramid

If you split the triangle into 2, you can use Pythagoras… Starter Calculate the Area of these Triangles. You will need to think carefully on the second one… If you split the triangle into 2, you can use Pythagoras… 6cm 6cm 7cm 8cm 5.196cm 3cm 6cm base x height 2 c2 – b2 = a2 5cm 62 – 32 = a2 base x height 2 6 x 5.196 2 27 = a2 5 x 7 2 5.196… = a = 17.5cm2 = 15.59cm2

Surface Area of a Pyramid Today we are going to look at finding the Surface area of Pyramids This will involve the use of Pythagoras’ Theorem like we saw in the starter This topic is graded A/A* depending on the difficulty of the question!

Surface Area of a Pyramid Find the Surface Area of this Pyramid As all the lengths are the same, all sides are the same. Therefore all you need to do is find the area of one side, then multiply by 4 c2 – b2 = a2 Sub in c and b 82 – 42 = a2 8cm 8cm Work out the left side 8cm 48 = a2 6.93cm Square root 6.93… = a 4cm 8cm base x height 2 Remember throughout this you should keep using the exact values in your calculator, rather than the rounded ones! Sub in the base and height 8 x 6.93 2 Work out the sum = 27.71cm2 Multiply by 4 as there are 4 sides = 110.85cm2

Surface Area of a Pyramid Find the Surface Area of this Pyramid c2 – b2 = a2 7m Sub in c and b 7m 7m 72 – 52 = a2 Work out the left side 24 = a2 4.9m Square root 4.9 = a 5m 10m 10m base x height 2 Sub in the base and height 10 x 4.9 2 Work out the sum = 24.49m2 Multiply by 4 as there are 4 triangular sides = 97.98m2 10 x 10 = 100m2 Don’t forget the base! 100m2 + 97.98 = 197.98m2

Summary We have recapped our knowledge of Pythagoras’ Theorem We have looked at how to use this to work out the Surface Area of Pyramids