Question

The figure shows the layout of a regular triangular pyramid. Calculate how many square centimetres of paper are needed to make this pyramid.Give your answer to the nearest square centimetre.

Answer 1

#a)

Since the net of the regular pyramid is formed from 4 equilateral triangles, then the surface area of the pyramid is 4 x the area of 1 triangle

The rule of the area of the equilateral triangle is

`A=(√(3))/(4)s^2`

Where s is the length of the side of the triangle

Since the length of the side of the triangle is 20 cm, then

s = 20

Substitute the value of s in the rule above

`\begin{gathered} A=(√(3))/(4)*(20)^2 \\ \\ A=(√(3))/(4)*400 \\ \\ A=100√(3)\text{ cm}^2 \end{gathered}`

Now to find the surface area of the pyramid multiply the area of 1 triangle by 4

`\begin{gathered} S.A=4*100√(3) \\ S.A=400√(3) \\ S.A=692.820323\text{ cm}^2 \end{gathered}`

Round it to the nearest square m (whole number)

S.A = 693 cm^2

You need 693 square cm to make the pyramid