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Geometry ,Graph theory Points, lines, planes, and angles, Polygons, Perimeter
,area, Volume and also Graphs, paths, and circuits, Euler paths and Euler circuits
1.
1. Use the figure below to find the following:
IBD ∩
←→
IJ
DBI ∩
◦→
FC
___
__
___
BC U CF U FB
2. ∠PQR and ∠ABC are supplementary angles and ∠PQR is nine times as large as
∠ABC. Determine the measure of each angle. Students must show all work step by step
to receive full credit for the problem.
3. What is the exact area of a circle with a diameter of 11 inches?
The following triangles, Δ ABC and Δ DEF, are congruent.
Find the lengths of all missing sides and measures of all angles for
both triangles. Include correct units with each of your answers.
First triangle:
Second triangle:
Side AB =
Angle BAC =
Side DF =
Side EF =
Angle ABC =
Angle DEF =
Angle EFD =
5. Find the area of a trapezoid with a height of 4 m and bases of 13 m and 22 m.
6. A recreation room has the following dimensions. Carpeting will cost
$1.50 a square foot. How many square feet of carpet will be needed and
how much will it cost? Include correct units at each stage within your
solution.
7. Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the
longest side is 52 mm. Include correct units with each part of your solution
8. How many cubic centimeters can a cigar box hold if its dimensions are
4 centimeters by 13 centimeters by 8 centimeters? Include correct units
with your solution.
9. An ice cube that measures 2.4 centimeters on each side contains how
many cubic centimeters of ice? Include correct units with your
solution.
Find the approximate value of the volume of the right circular cone with a circular base shown
below. Approximate your solution to the nearest hundredth.
11. In a 9 inch square cake pan and a 10 inch square cake pan, what is
the difference in volume each pan will hold? Assume each pan is 2
inches high. Show step by step work. Include correct units with your
solution.
12. For the following floor plan, determine whether it is possible for a
person to walk through each doorway without using any of the doorways
twice. If it is possible, state such a path. If it is not possible,
answer, "not possible."