Starter• Calculate the Area of these Triangles. You will

need to think carefully on the second one…

8cm

5cm

7cm

6cm

base x height 2

5 x 7 2 =

17.5cm2

3cm

6cm6cm

c2 – b2 = a2

62 – 32 = a2

27 = a2

5.196… = a

5.196cm

base x height 2

6 x 5.196 2

= 15.59cm2

If you split the triangle into 2, you

can use Pythagoras…

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

8cm

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

8cm

8cm 8cm

4cm

c2 – b2 = a2

82 – 42 = a2

48 = a2

6.93… = a

Sub in c and b

Work out the left side

Square root6.93cm

base x height 2

8 x 6.93 2=

27.71cm2=

110.85cm2

Sub in the base and height

Work out the sumMultiply by 4 as

there are 4 sides

Remember throughout this you should keep

using the exact values in your calculator,

rather than the rounded ones!

Surface Area of a Pyramid• Find the Surface Area of this Pyramid

10m

7m7m 7m

10m5m

c2 – b2 = a2

72 – 52 = a2

24 = a2

4.9 = a

Sub in c and b

Work out the left side

Square root4.9m

base x height 2

10 x 4.9 2

= 24.49m2

= 97.98m2

Sub in the base and height

Work out the sumMultiply by 4 as there

are 4 triangular sides

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