Verify using eluer's formula
a] Triangular pyramid
b] Triangular prism
Answers
A) Triangular pyramid
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.
B) Triangular prism
Consider the triangular prism shown
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.
Hope it helps you dear
Answer:
TRIANGULAR PYRAMID
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.
TRIANGULAR PRISM
Consider the triangular prism shown
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.
