Question

Verify euler's formula for a triangular pyramid

Answer 1

Solution :-

A triangular pyramid has 4 faces, including the base, are triangles, 4 veritces and 6 edges.

Faces = 4

Vertices = 4

Edges = 6

F + V = E + 2

F + V - E = 2

This relationship is called Euler's Formula.

⇒ 4 + 4 - 6 = 2

⇒ 8 - 6 = 2

⇒ 2 = 2

L.H.S. = R.H.S.

Hence, The Euler's Formula is verified for a Triangular Pyramid.

Answer 2

Recall the Euler’s formula, F + V = E + 2

Here number of faces, F = 5

Number of vertices, V = 6

Number of edges, E = 9

Consider, F+V = 5 + 6 = 11

E + 2 = 9 + 2 = 11

Hence F + V = E + 2

Thus Euler’s formula is verified.

Euler's formula, named after Leonhard Euler, is a scientific equation in a complex investigation that sets up the key connection between the trigonometric capacities and the unpredictable exponential capacity.