Polyhedra, Patterns, and Surface Area
Volumes of Solid Shapes
Transformations and Symmetry
Congruence
Dilations and Similarity
100
Name the five platonic solids, and the number of faces each has.
Tetrahedron (4), Cube (6), Octahedron (8), Dodecahedron (12), Icosahedron (20)
100
What is the volume of a cube that has an edge of length 6 cm?
216 cm3
100
Does every rectangle have 4-fold rotational symmetry? If so, explain why. If not, is there a rectangle that has this property?
Not all rectangles have 4-fold rotational symmetry, but all rectangles that are squares do.
100
True or False: There exist two quadrilaterals with the same side lengths that are not congruent.
True.
100
True or false: All squares are similar.
True
200
Find the surface area of a regular octahedron with the property that one of its faces has one side length equal to 6 inches.
72\sqrt(3)
square inches
200
Consider a right prism with a volume of 256 cubic units and a height of 16 units. Find the area of one of the bases.
16 square units.
200
Find a figure with infinitely many lines of symmetry.
Any circle works.
200
Suppose there exist two congruent equilateral triangles, one with at least one side length equal to 9 feet. Find the perimeter of the other.
27 feet.
200
If I'm 5 feet tall and in a printed picture of myself and a friend, I measure 4 inches and he measures 5 inches, how tall is my friend?
6 feet, 3 inches.
300
How many edges does an oblique hexagonal prism have?
18 edges (note that obliqueness is irrelevant here)
300
I'll draw a solid on the board. Find its volume.
(The correct volume)
300
Consider the triangle with vertices at (1, 4), (2, 3), and (2, 5). After reflecting the triangle across the line y = 2, what are the coordinates of its vertices?
(1, 0), (2, 1), and (2, -1).
300
We have seen that SSA (Side-Side-Angle) is not a valid congruence criterion for arbitrary triangles. However, there is a measure of the known angle that makes this a valid criterion. What is that measure?
90o
300
In the figure below, suppose that the length of line segment AB is 36 units, that line segment BD has length 48 units, and that line segment BC has length 40 units. Find the length of line segment DE.
10 units.