Networks & Euler's Formula (Grade 10)

Free printable Grade 10 worksheet on networks and Euler's formula for connected planar graphs.

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Grade 10 · Math worksheet

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Math

Space: Networks & Euler's Formula

Use Euler's formula for connected planar networks (V - E + F = 2) to find the missing value.

1.
A connected planar network has 6 vertices and 8 edges. Using Euler's formula (V - E + F = 2), find the number of faces F (including the outer region).
2.
A connected planar network has 9 edges and 4 faces (including the outer region). Using Euler's formula (V - E + F = 2), find the number of vertices V.
3.
A connected planar network has 6 edges and 3 faces (including the outer region). Using Euler's formula (V - E + F = 2), find the number of vertices V.
4.
A connected planar network has 5 edges and 2 faces (including the outer region). Using Euler's formula (V - E + F = 2), find the number of vertices V.
5.
A connected planar network has 5 vertices and 4 faces (including the outer region). Using Euler's formula (V - E + F = 2), find the number of edges E.
6.
A connected planar network has 7 vertices and 4 faces (including the outer region). Using Euler's formula (V - E + F = 2), find the number of edges E.

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