# Geometry problems

What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each.

We can use the Pythagorean theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of the theorem.

1. PQR and ABC are complementary angles and PQR is nine times as large as  ABC. Determine the measure of each angle.

2. If line l and m are parallel, find the measure of 6.

3. (Using ABC, find the following:

a) The length of side AC

b) The perimeter of ABC

c) The area of ABC

4. A diagonal walk through a rectangular rose garden 18 meters by 24 meters can be built at $12 per linear meter. How much will the walk cost?

5. Sam wishes to fertilize his lawn that is 16 yards by 70 yards. The organic fertilizer costs $5.75 per bag. Each bag covers 525 square feet. What is the cost to fertilize his yard?

6. What is the area and circumference of a circle with diameter 22 mm? (Give exact solutions. Include correct units with each!)

7. A drinking glass is in the shape of a cylinder that is 5 cm in diameter and 140 mm tall. How many cubic centimeters of water will it hold? (Approximate solution to the nearest tenth.)

8. Create a graph with precisely two odd vertices and two even vertices. State which of your vertices are even and which are odd. Use a dot and letter to mark each vertex.

9. 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, determine such a path.

10. Use the figure below to find the following:

i. mÐHBD + mÐBGI + mÐGCA = ____

ii. BG U GC U CB

iii. ÐGCB ∩ BH

iv. ÐABG ∩ BD

11. (2 pts) A. Find the supplementary angle of 34

A. 146 B. 56 C. 34 D. 68

B. ABC and PQR are supplementary angles and ABC is eleven times as large as PQR. Determine the measure of each angle.

12. Lines l and m are parallel and are cut by the transversal shown. Determine the measures of angles 1 through 7.

13. Find the perimeter and area of a right triangle if the shortest side is 7 cm and the longest side is 25 cm.

14. What is the area in feet of circular tablecloth that has a diameter of 42 inches?

A) 1385.44236 square feet B) 21 square feet C) 3.0625 square feet D) 1.75 square feet

15. Find the volume of a refrigerator that is a rectangular solid and is 2 meters tall and has a base that is 1.2 meters square.

A) 1.44 cubic meters B) 2.4 cubic meters C) 2.88 cubic meters D) 3.2 cubic meters

16. A conical water tank has a base with a diameter of 6 ft and is 10 ft tall. How many gallons of water will the tank hold? Round your solution to the nearest hundredth. (1 cubic foot holds about 7.480519 gallons)

17. Find the volume of a pyramid that has a height of 12 meters and a square base 11 by 11 meters. Include correct units.

18. Find the volume of the figure below with a circular base shown below. Give answer

a. exactly and b. approximated to the nearest hundredth.

19. a) Find the area of a trapezoid with a height of 6 m and bases of 14 m and 21 m

b) Find the perimeter of the parallelogram below.

20. A recreation room has the following dimensions. Carpeting will cost $8.00 a square yard. How many square yards of carpet will be needed and how much will it cost?

5 yd

11 yd

4 yd

4 yd

21. The following triangles,  ABC and  DEF, are congruent.

A

E

F D

B C

Find the lengths of all missing sides and measures of all angles for both triangles.

Please fill in the blanks:

First triangle: Second triangle:

Side AB = Side DF =

Angle BAC = Side EF =

Angle ABC = Angle DEF =

Angle EFD =

22. Create a graph with five vertices, no bridge, and a loop.

#### Solution Summary

Step by step solutions to all the problems are provided.