An archeologist was digging around the pyramids of ancient Egypt. He discovered a mummie covered in chocolate and nuts.

On further investigation the mummie was identified as pharaoh roche.

This is the clue to our topic.

We are going to look at the surface area of pyramids here.

Surface area is the area of each face of the pyramid added together.

Before we are ready to go there are a few things to remember

Area of a square = base x height

Area of a rectangle = base x height

Area of a triangle = base x height ÷ 2

Example 1

This pyramid has a side length of 4 cm and it's height is 5 cm.

__To find the surface area of this square based pyramid we__

1. Calculate the area of the base 4 x 4 = 16 cm²

2. Find the area of one of the triangular sides 4 x 5 ÷ 2 = 10 cm²

3. There are four sides to the pyramid so 10 x 4 = 40 cm²

4. Add the total area of the sides to the area of the base = 16 + 40 = 56 cm²

Example 2

This triangular based pyramid has base 6 cm height 8 cm

__To find the surface area of this triangular based pyramid we__

1. Calculate the area of the base 6 x 8 ÷ 2 = 24 cm²

2. There are four sides to the pyramid (the base and three sides) so 24 x 4 = 96 cm²

The sides base has sides of 5 cm and 6 cm. The height of the pyramid 6 cm.

__To find the surface area of this rectangular based pyramid we__

1. Calculate the area of the base 5 x 6 = 30 cm²

2. We find the area of the triangle with the base of 5 cm, 5 x 6 ÷ 2 = 15 cm²

3. The face opposite has the same area so multiply by 2. 15 x 2 = 30 cm²

4. Now find the area of the triangle with the base of 6 cm. 6 x 6 ÷ 2 = 18 cm²

5. The face opposite has the same area so multiply by 2. 18 x 2 = 36 cm²

Where do Pharaoh's like to eat?

Pizza Tut