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Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Polyhedra (Questions)

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In Math, a 3-D (solid) shape made by fitting polygons together is called a polyhedron. You have already met some polyhedra, e.g. cuboids. A regular polyhedron is formed from regular polygons all the same size and shape.

Which of these shapes is not a polyhedron?

[ ]	Cube
[ ]	Pyramid
[ ]	Sphere
[ ]	Triangular prism

The polygons forming the surface of a polyhedron are called .......

[ ]	areas
[ ]	edges
[ ]	faces
[ ]	sides

Where the straight sides of two polygons meet on the surface of a polyhedron they form a(n) .......

[ ]	area
[ ]	edge
[ ]	line
[ ]	side

The place on the surface of a polygon where several edges meet is called a .......

[ ]	corner
[ ]	dent
[ ]	point
[ ]	vertex

What is the name of the regular polyhedron in which four equilateral triangles meet at each vertex?

[ ]	Hexahedron
[ ]	Icosahedron
[ ]	Octahedron
[ ]	Tetrahedron

If you add the number of faces of a polyhedron to the number of its vertices the result is always .......

[ ]	equal to the number of edges
[ ]	2 more than the number of edges
[ ]	2 less than the number of edges
[ ]	1 more than the number of edges

How many edges has a pyramid with a hexagonal base?

[ ]	6
[ ]	8
[ ]	10
[ ]	12

How many faces has the regular polyhedron made with pentagons?

[ ]	5
[ ]	10
[ ]	12
[ ]	15

A polyhedron with four rectangles or squares meeting at each vertex is called .......

[ ]	a cuboid
[ ]	a parallelepiped
[ ]	a trapezoid
[ ]	impossible

10.

A polyhedron formed from rectangles set at right-angles to a polygonal base and top is called a .......

[ ]	parallel
[ ]	prism
[ ]	prune
[ ]	pyramid

Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Polyhedra (Answers)

Which of these shapes is not a polyhedron?

[ ]	Cube
[ ]	Pyramid
[x]	Sphere
[ ]	Triangular prism

Polyhedra have straight edges and flat surfaces

The polygons forming the surface of a polyhedron are called .......

[ ]	areas
[ ]	edges
[x]	faces
[ ]	sides

Where the straight sides of two polygons meet on the surface of a polyhedron they form a(n) .......

[ ]	area
[x]	edge
[ ]	line
[ ]	side

The place on the surface of a polygon where several edges meet is called a .......

[ ]	corner
[ ]	dent
[ ]	point
[x]	vertex

What is the name of the regular polyhedron in which four equilateral triangles meet at each vertex?

[ ]	Hexahedron
[ ]	Icosahedron
[x]	Octahedron
[ ]	Tetrahedron

Imagine two square-based pyramids stuck together

If you add the number of faces of a polyhedron to the number of its vertices the result is always .......

[ ]	equal to the number of edges
[x]	2 more than the number of edges
[ ]	2 less than the number of edges
[ ]	1 more than the number of edges

V + F = E + 2 is a formula discovered by the Swiss mathematician Leonhard Euler

How many edges has a pyramid with a hexagonal base?

[ ]	6
[ ]	8
[ ]	10
[x]	12

Use Euler's formula with F = 7 and V = 7

How many faces has the regular polyhedron made with pentagons?

[ ]	5
[ ]	10
[x]	12
[ ]	15

This is called a dodecahedron

A polyhedron with four rectangles or squares meeting at each vertex is called .......

[ ]	a cuboid
[ ]	a parallelepiped
[ ]	a trapezoid
[x]	impossible

When four right angles meet at a point they completely fill the flat space so they cannot be folded into a solid

10.

A polyhedron formed from rectangles set at right-angles to a polygonal base and top is called a .......

[ ]	parallel
[x]	prism
[ ]	prune
[ ]	pyramid

The cross section of a prism is the same shape and size along its whole length