Use Euler’s formula to answer question.
1 answer:
Answer: The correct option is (C) 38.
Step-by-step explanation: Given that a polyhedron has 20 vertices and 20 faces.
We are to find the number of edges of the polyhedron using Euler's formula.
<em><u>Euler's formula :</u></em>
For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges.
Mathematically, V − E + F = 2, where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.
For the given polyhedron, we have
number of vertices, V = 20,
number of faces, F = 20
and
number of edges, E = ?
Therefore, from Euler's formula
.
Thus, the required number of edges of the given polyhedron is 38.
Option (C) is CORRECT.
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Area of sandbox = 169 square feet
Area of square with side 'x' is given by the formula =
We have to determine the total length of wood Drew needs to make the sides of the sandbox.
Total length of wood required would be equal to perimeter of sandbox.
Let 'a' be the side of the square sandbox.
So, Area of sandbox = 169
a = 13 feet
Total length of wood required to make sides of the sandbox = Perimeter of the square sandbox =
=
= 52 feet.
Therefore, 52 feet of wood is required to make the sides of the square sandbox.