Math Practice Problems for Seventh Grade in Geometry

7G-17) Answer: 5 trips

Jeremy and Josh had just gotten admitted to the SWIS Program (Summer Work in Space). The alien in charge told them they would need skypacks and checked to make sure they weren't afraid of flying! Their job was to clean the front window wall of the First Interspace Congressional Building. The wall measured 700 feet by 800 feet. Using their skypacks they decided to go around the wall beginning at one corner and cleaning a 10-foot area, working their way toward the center of the wall. How many trips around the wall did they make before they cleaned 1/4 of it?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-16) Answer: 5 times

Sue is watching her Uncle George lay down sod in Carver Park. He must cover an area 40 feet square, but he wants to leave a square in the center of the lawn, equaling one fourth of the total area. Sue gets to plant that central area with marigolds, her favorite flowers. The sod that Uncle George is laying down comes in widths of 2 feet. If he starts unrolling the sod at one corner of the square and continues unrolling it around the edge, working his way toward the center, how many trips around the square will he make with the sod?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-15) Answer: 10

Mombasa is on the swim team. He swims his first 3 laps without weights and the next 5 laps with weights. Jamie is also on the swim team, but she swims her first 5 laps with weights and her next 3 laps without. If Mombasa and Jamie each swim 40 laps, using their own patterns of carrying weights, during how many laps will they both be using weights at the same time?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-14) Answer: 6 and part of 7^th

Bella and Jana's billboard business is really taking off. They just got a new assignment, cleaning the billboard for Hugo's Hut. The billboard is 45 feet by 90 feet and they decide to each do 1/2 the job. Bella and Jana take turns with a squeegee 2 1/2 feet wide, beginning at an outside edge and going all the way around, working their way toward the center. When it gets dark and they have to quit, they have completed 4/5 of the billboard. How many trips have they made around the billboard with their squeegee?   Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-13) Answer: 123.6 square inches

A manufacturer of novelty buttons uses square sheets of metal that are 24 inches on each side. The press punches out 144 circular buttons, each with a diameter of 2 inches, from a sheet. How much metal is wasted from each sheet?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-12) Answer: 5+p square feet

A square mile of land (1 x 1) has become contaminated. The Environmental Protection Agency has regulated that no one can live within one mile of any point in the contaminated area. Find the area of the uninhabitable land.  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-11) Answer: 6x6x6 units

Find the dimensions of a cube whose volume is numerically the same as its surface area.  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-10) Answer: 3x6; 4x4

Find the dimensions of all rectangles such that their perimeter and area are numerically equal. (Consider only integral answers.)  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-9) Answer: 304 seats

Jesse has a season's subscription to the local drama theater. His seat is in the 5th row from the front and the 12th row from the back of the theater. His seat is 8 seats from the right aisle and 12 seats from the left aisle. If each row has the same number of seats, how many seats are in the entire theater?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-8) Answer: 14 bracelets

Lucille makes copper bracelets to sell at the local crafts show. Each bracelet requires a rectangular strip of hammered copper that is 5" x 7". She buys the copper in rectangular sheets that measure 21" x 24". What is the maximum number of bracelets she can get from a single sheet of copper?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-7) Answer: 27 feet

Mike puts 104 feet of plastic edging around the perimeter of Mrs. Flores's garden in order to make it easy to trim. If her garden is in the shape of a rectangle with a length of 25 feet, how wide is it?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-6) Answer: 233 ways

Mr. Fondel is going to build a path from his house to the front walk. The path will be 2 feet wide and 12 feet long. He intends to lay paving blocks along the path. Each paving block is in the shape of a rectangle that is 2 feet by 1 foot. In how many different ways can Mr. Fondel lay the blocks along the path?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-5) Answer: yes - height 6.33 feet or 6 feet and 4 inches

The floor of a storage shed is a rectangle with an area of 99 square feet. The volume of the shed is advertised as 627 cubic feet. Lawrence is six feet, three inches tall. Can Lawrence stand upright in the storage shed?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-4) Answer: about $6000

The new playing field behind the school is in the shape of a rectangle that is 80 yards long and 50 yards wide. On each of the shorter sides, there is a semi-circle whose diameter is the shorter side. Approximately how much will it cost to sod the new field if sod costs $1 per square yard?   Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-3) Answer: triangle

The school Spirit Club is having a fund-raising drive. You have been appointed chairperson, and have been given the job of preparing tags to sell on Spirit Day to raise fund. You have a piece of bright green material that is rectangular in shape and measures 18 inches by 45 inches. Members of your committee have suggested four different shapes for the tags: 1) A circle with a one-inch diameter, to sell for $1.25 each 2) A one-inch square, to sell for $1.25 each 3) An equilateral triangle with a one-inch side, to sell for 75 cents each 4) A one-inch by two-inch rectangle, to sell for $2.50 each Which shape would you use to earn the most money? How much would you earn? Defend your decision.  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-2) Answer: 1 – no faces; 6 – one face; 12 – two faces; and 8 – three faces

A 3x3x3 cube is made from 27 smaller cubes. Suppose all of the faces of the large cube are painted red and then it is taken apart. How many of the small cubes would have no faces painted red? One face painted red? Two faces painted red? Three faces painted red?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7G-1) Answer: Dimensions: 12 in by 8 in by 6 in

One face of a rectangular box has an area of 96 square inches. Another face is 72 square inches and the other face is 48 square inches. What are the dimensions of the box?  Explain in detail how you found your answer using words, numbers, and/or pictures.

Share a problem (thank you) to add to this list and submit to:   donna_buck@pasd.wednet.edu Please title the subject "Problems for 7G" and include the answer.