# Solutions to problems in geometry

See attached file for full problem description.

1. Use the figure below to find the following:

2. a) Find the complementary angle of 26

b) DEF and GHI are supplementary angles and GHI is fourteen times as large as DEF. Determine the measure of each angle

3. Lines A and B are parallel and are cut by the transversal shown. Determine the measures of angles 1 through 7.

4. Find the perimeter and area of a right triangle if the shortest side is 9cm and the longest side is 15cm.

5. What is the circumference and area in feet of circular pool that has a diameter of 20 yards?

6. Find the volume of a rectangular bread box that is 9 inches tall and has a base that is 18 inches by 12 inches.

A) 1296 cubic inches B) 1944 cubic inches C) 2916 cubic inches D) 648 cubic inches E) 3888 cubic inches

7. A cylindrical water tank has a base with a diameter of 2 ft and is 4 ft tall. How many gallons of water will the tank hold? (1 cubic foot equals 7.5 gallons)

8. Find the volume of a sphere that has a diameter of 9 meters.

A) 243 m3 B) 486 m3 C) 121.5 m3 D) 972 m3

9. Find the volume of the pyramid shown below.

10. a) Find the area of a trapezoid with a height of 9 m and bases of 7 m and 25 m

b) Find the perimeter of a parallelogram with sides measuring 6.5 m and 3.5 m

11. 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?

12. The following triangles are congruent.

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

13. Create a graph with seven vertices, a bridge, and a loop.

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#### Solution Summary

The solution contains detailed answers to various questions in geometry like perimeter, circumference, Pythagoras theorem and the volume of pyramid.