Question

The table shows information about the faces, edges and vertices for some pyramids.

Shape of base Faces Edges Vertices
Triangle 4 6 4
Square 5 8 5
Pentagon 6 10 6
Hexagon 7 12 7

Write a formula that connects the number of sides of the base, S,
with the number of edges, E.
Hence, work out the number of edges a pyramid with a 30-sided base has.

Answer 1

Answer:

E = 2S

Step-by-step explanation:

S = Number of sides in base

E = Number of edges

1) Triangle -

Numbers of sides in base = 3 = S

Number of edges = 6 = E

E = 2S

2) Square

Number of sides in base = 4 = S

Number of edges = 8 = E

E = 2E

3) Pentagon

Number of sides in base = 5 = S

Number of edges = 10 = E

S = 2E

4) Hexagon

Number of sides in base = 6 = S

Number of edges = 12 = E

E = 2S

Hence proved. E = 2S

Pyramid with 30 - sided base -

Number of sides in base = 30 = S

Number of edges = E = 2S = 30 x 2 = 60 edges