# Geometry - Parallelograms and Triangles

Please solve. See the attached file for diagrams.

Question 1

The preferred seating area at the Music Theatre is the shape of a parallelogram. Its base is 34 yd and its height is 39.6 yd. Find the area.

Question 2

The diagonal of a small pasture measures square root 12,617 feet in length. Find the length of this diagonal to the nearest tenth of a foot. Use a calculator or a square root table when needed.

Question 3

A rectangular plot of land is 71 meters by 87 meters. Find the length of the diagonal. Round to the nearest tenth.

Question 4

A radio station sends out waves in all directions from a tower at the center of the circle of broadcast range. The broadcast range has a diameter of 196 miles. Determine how large an area is reached. Use pi ~= 3.14 and round to the nearest hundredth.

Question 5

Juliet runs out of gas in Barnhaven, South Carolina. She walks 9 mi west and then 5 mi south looking for a gas station. How far is she from her starting point? Round to the nearest tenth.

Question 6

See the above figure. Find the measure of the angle: <DGF

Question 7

A new pyramid has been found in South America. The pyramid has a rectangular base that measures 62 yd by 180 yd, and has a height of 100 yd. The pyramid is not hollow like the Egyptian pyramids and is composed of layer after layer of cut stone. The stone weighs 432 lb per cubic yard. How many pounds does the pyramid weigh?

Question 8

A dentist places a gold filling in the shape of a cylinder with a hemispherical top in a patient's tooth. The radius of the filling is 3 mm. The height of the cylindrical portion is 4 mm. If dental gold costs $16.00 per cubic millimeter, how much did the gold for the filling cost? Round to the nearest cent. Use pi ~= 3.14.

Question 9

A courtyard is shaped like a parallelogram. Its base is 132 yd and its height is 61 yd. Find its area.

Solve. Round to the nearest tenth when necessary.

Question 10

Jack and Jill are planning a new kitchen. The old kitchen measured 12 feet by 18 feet. The new kitchen is similar in shape, but the longest dimension is 21 feet. What is the smaller dimension of the new kitchen?

Question 11

The above circle graph displays Chris and Mary Smith's monthly $2900 family budget. Use the circle graph to answer the question: What is the ratio of money spent on rent to the total amount of the monthly budget?

Question 12

The above double-bar graph illustrates the revenue for a company for the four quarters of the year for two different years. Use the graph to answer the question: What was the difference in revenue between the third quarter of 1999 and the third quarter of 2000?

Question 13

The above line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. If the temperature continues to decrease by the same amount as from 5 p.m. to 6 p.m., what will the temperature be at 9 p.m.?

Question 14

A new car dealership has taken an inventory of the vehicles it has in stock. Above is a histogram indicating the number of vehicles in stock in certain price ranges. Use the histogram above to answer the question. What percent of the 75 vehicles in stock were priced between $21,000 and $27,999?

Question 15

Each number below is the number of miles the Hoover family has driven in a week. Determine the frequency of the class interval for this data.

142 284 557 354 315

265 329 157 379 294

425 498 198 297 414

210 342 171 416 305

A) Miles Driven

(Class Interval) Tally Frequency

130-264 miles ___________ ___________

B) Miles Driven

(Class Interval) Tally Frequency

265-329 miles ___________ ___________

C) Miles Driven

(Class Interval) Tally Frequency

330-379 miles ___________ ___________

D) Miles Driven

(Class Interval) Tally Frequency

380-444 miles ___________ ___________

E) Miles Driven

(Class Interval) Tally Frequency

460-474 miles ___________ ___________

Question 16

The grades are given for a student for a particular semester. Find the grade point average. Assume the grade point values are A = 4, B = 3, C = 2, D = 1, and F = 0. Round to the nearest tenth when necessary.

Grade Credit Hours

B 2

A 3

C 1

B 4

A 2

Question 17

The numbers of minutes Maria spent looking on the internet for gifts for her family during the last six days are as follows: 5, 8, 28, 21, 31, 46. Find the median. Round to the nearest tenth when necessary.

Question 18

The last seven computer games sold at the local electronics store cost $20, $ 34, $46, $ 34, $49, $ 34, $49. Find the mode.

Question 19

19. A.) On the morning of December 19 the temperature was -4 degrees F. The next morning the temperature had risen 20 degrees F. What was the temperature on the morning of December 20? B.) On the morning of February 2 the temperature was 14 degrees F. The next morning the temperature had dropped 20 degrees F. What was the temperature on the morning of February 3?

Question 20

Perform the indicated operations in the proper order: -17 - ( -2)( -6) + (- 24)/( -3)

Question 21

1/3 / (-4/7)(-1/6) + (-1/18)

Question 22

8.38 x 107 feet - 5.84 x 107 feet

Question 23

Write the equation without multiplication signs: C = 2 x pi x r

Question 24

Simplify: -7( 8x - 2y) - 5(-x + 4y)

Question 25

Solve: 1.3y + 4.4 = 0.8y + 4.1

Question 26

Translate the English sentence into an equation using the variables indicated: The ratio of brick houses to wooden houses in a particular city is 5 to 11. Let b = the number of brick houses and w = the number of wooden houses.

Question 27

For three days in a row, volunteers picked up trash on a particular beach. They picked up a total of 921 pounds. On the second day they collected 39 pounds more than on the first day. On the third day, they picked up 18 pounds less than on the first day. How many pounds of trash did they pick up on the first day?

Question 28

A rental agent for vacation houses in southern Spain earns a flat amount of base pay per month plus a 7.5% commission on rentals sold during that month. One month he earns $5575 on rental sales of $45,000. What is his base monthly pay?

Question 29

A poster in the shape of a triangle has one side that is five inches more the length of the shortest side, and another side that is three inches less than twice the shortest side. Find the dimensions of the poster if its perimeter is 42 inches.

Question 30

A triangle has three angles, R, S, and T. Angle T is 40 degrees greater than angle S. Angle R is 8 times angle S. What is the measure of each angle?

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#### Solution Summary

This is a series of geometry problems regarding parallelograms and triangles. Each question is addressed step by step in an attached Word file.

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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