Verify Euler’s form forA.Square pyramidB.Triangular prismC.Rectangular prism

To verify Euler’s formula for different polyhedra, we use the formula:

V - E + F = 2

where:

V is the number of vertices,
E is the number of edges, and
F is the number of faces.
Let's analyze each of the given polyhedra:

A. Square Pyramid
A square pyramid consists of:

5 vertices (4 at the base and 1 at the apex),
8 edges (4 edges at the base and 4 edges connecting the base to the apex),
5 faces (1 square base and 4 triangular faces).
Using Euler's formula:

V = 5
E = 8
F = 5
Now, check Euler's formula: 5 - 8 + 5 = 2

So, Euler’s formula holds true for the square pyramid.

B. Triangular Prism
A triangular prism consists of:

6 vertices (3 at each triangular base),
9 edges (3 edges at the bottom base, 3 at the top base, and 3 connecting the corresponding vertices of the two bases),
5 faces (2 triangular faces and 3 rectangular faces).
Using Euler's formula:

V = 6
E = 9
F = 5
Now, check Euler's formula: 6 - 9 + 5 = 2

Euler’s formula holds true for the triangular prism.

C. Rectangular Prism
A rectangular prism consists of:

8 vertices (each corner of the rectangular prism),
12 edges (4 edges on each of the 3 rectangular faces),
6 faces (all rectangles).
Using Euler's formula:

V = 8
E = 12
F = 6
Now, check Euler's formula: 8 - 12 + 6 = 2

Euler’s formula holds true for the rectangular prism.

Conclusion:
Euler's formula is verified for all the given polyhedra:

Square Pyramid: V - E + F = 2
Triangular Prism: V - E + F = 2
Rectangular Prism: V - E + F = 2