Perimeter, Area, Volume

Triangles, Squares, Rectangles, Circles

1. The top surface of a rectangular table has an area of 100 square feet and a width of 5 feet. What is the length, in feet, of the surface?

2017 June(74C) Math Question 1

2012 December(71A) Math Question 1

2011 June(69F) Math Question 1

2012 June(70C) Math Question 2

2. The length of a rectangle is 12 feet. The width of the rectangle is 1/2 the length. What is the perimeter of the rectangle, in feet?

2016 April(73E) Math Question 2

2. The statement AABC ADEF is true. Which of the following statements must be true?

2016 December(74H) Math Question 2

2012 December(71A) Math Question 3

2013 April(71G) Math Question 3

2019 April(Z15) Math Question 4

2012 December(71A) Math Question 4

5. A carnival game is played using an open box with a rectangular bottom measuring 6 inches by 13 inches. A square with side lengths of 4 inches is painted on the bottom of the box. The game is played by dropping a small bead into the open box. if the bead conies to rest in the painted square, the player wins a prize. Assuming a bead dropped into the box comes to rest at a random spot on the bottom of the box, which of the following is closest to the probability that the bead comes to rest in the painted square?

2018 April(A09) Math Question 5

5. Carlotta is helping her grandfather center a large framed picture on his living room wall. As shown in the figure below, the rectangular wall is 24 feet long, and the rectangular framed picture is 4.5 feet high and 7.5 feet long. The left edge of the frame will be x feet from the left edge of the wall, and the right edge of the frame will be x feet from the right edge of the wall. What is the value of x? DO YOUR FIGURING HERE.

2013 June(71C) Math Question 5

2018 December(B05) Math Question 5

2012 June(70C) Math Question 5

2009 April(66F) Math Question 6

2009 December(68A) Math Question 7

2020 July(C01) Math Question 10

10. Rectangle A has a length of 64 inches and a width of 48 inches. Rectangle B has a length and a width that are both 3/4 times the length and the width of Rectangle A. Rectangle C has a length and a width that are both 3/4 times the length and the width of Rectangle B. What is the perimeter, in inches, of Rectangle C ?

Perimeter of Rectangle

2021 April(D05) Math Question 10

2009 June(67C) Math Question 10

11. Two sides of a triangle are equal in length. The third side is 3 centimeters longer than either of the other 2 sides. Given that the perimeter of the triangle is 93 centimeters, what is the length, in centimeters, of the longest side?

2018 April(A09) Math Question 11

11. Banu will build a fence around a rectangular 30-foot-by-25-foot play area. Given that fencing costs $4.05 per foot, how much will the fencing cost for Banu to completely surround the play area?

2020 December(D03) Math Question 11

12. The side lengths, in centimeters, of right triangle △DEF are given in the figure below. What is the area, in square centimeters, of △DEF ?

2014 April(71H) Math Question 12

2019 June(72F) Math Question 12

2013 April(71G) Math Question 12

2012 June(70C) Math Question 12

2010 April(68G) Math Question 12

12. In the Coaltown High School cafeteria, the student council is laying a triangular carpet in a corner that is designated to be a lounge. The carpet is a right triangle with the 2 shorter sides having lengths of 12 feet and 8 feet, as shown in the figure below. What is the area, in square feet, of the carpet?

2015 December(72E) Math Question 12

12. A king-sized inflatable rectangular bed when fully inflated will have inside dimensions, in inches, of 78 by 75 by 5. An air pump can pump air into the bed at a rate of 100  cubic inches per second. At that rate, which of the following is closest to the number of seconds it will take to fully inflate the bed?

Constant rate

Rectangular solids

2021 April(D05) Math Question 12

12. The dimensions of the rectangle shown below are given in inches. Which of the following expressions gives the area, in square inches, of the rectangle?

2016 April(73E) Math Question 12

12. The diagonal of a rectangular flat television screen is 26.0 inches. The width of the screen is 22.7 inches, and the height of the screen is 10.0 inches less than the width of the screen. Which of the following is closest to the area, in square inches, of the television screen?

Area of Rectangle(square)

2020 December(D03) Math Question 12

2012 June(70C) Math Question 13

14. The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 60 inches. What is the width of the rectangle, in inches?

2013 June(71C) Math Question 14

2013 December(71E) Math Question 14

2020 June(C02) Math Question 14

2013 April(71G) Math Question 15

2009 April(66F) Math Question 15

2020 July(C01) Math Question 15

15. In the figure below, the border of a pool and the border of a patio surrounding that pool are similar rectangles. The given dimensions are in feet. What is the length of the pool, in feet?

2015 April(73G) Math Question 15

2012 April(70G) Math Question 15

15. In the figure shown below, all angles are right angles, and the side lengths given are in inches. What is the area, in square inches, of the figure?

2021 December(E23) Math Question 15

2012 December(71A) Math Question 16

16. The area of a rectangular sheet of paper is 32 square inches. The length of the sheet of paper is twice its width. What is the perimeter, in inches, of the sheet of paper?

2014 June(72C) Math Question 16

16. A square and a rectangle have the same area. The length of the rectangle is 196 centimeters, and the width of the rectangle is 4 centimeters. What is the length, in centimeters, of a side of the square?

2021 June(D06) Math Question 16

17. What is the area, in square decimeters, of a right triangle with side lengths of 10 dm, 26 dm, and 24 dm ?

2018 April(A09) Math Question 17

17. A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long, 9 inches wide, and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of notepads that will fit in 1 closed box?

2015 June(73C) Math Question 17

2019 April(B04) Math Question 17

2012 April(70G) Math Question 17

2009 December(68A) Math Question 18

18. The vertices of PQR are given in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of nPQR ?

Area of Triangle

2021 April(D05) Math Question 18

19. An apartment building is 3 stories tall. Each story has 4 identical apartments. Each apartment’s living space consists of 4 rectangular rooms: a bathroom 8 feet by 10 feet, a kitchen 10 feet by 12 feet, a bedroom 12 feet by 12 feet, and a living room 12 feet by 14 feet. What is the area, to the nearest 1,000 square feet, of living space in the 3-story apartment building?

2014 April(71H) Math Question 19

2019 April(Z15) Math Question 19

2009 December(68A) Math Question 19

20. In the figure shown below, all angles are right angles, and the side lengths given are in feet. What is the area, in square feet, of the figure?

2018 April(A09) Math Question 20

20. The floor plan of Helena's kitchen is shown in the figure below; the given dimensions are in feet. Helena will install baseboard along the bottom of each wall (shown by solid lines in the floor plan). According to the floor plan, which of the following distances is closest to the perimeter, in feet, of Helena's kitchen?

2015 June(73C) Math Question 20

21. A triangle has a perimeter of 26 cm and sides of length x cm, (x + 3) cm, and (x + 5) cm. What is the value of x?

2018 April(A09) Math Question 21

21. A 5-inch-by-7-inch photograph was cut to fit exactly into a 4-inch-by-6-inch frame. What is the area, in square inches, of the part of the photograph that was cut off?

2015 June(73C) Math Question 21

21. Laura plans to paint the 8-foot-high rectangular walls of her room, and before she buys paint she needs to know the area of the wall surface to be painted. Two walls are 10 feet wide, and the other 2 walls are 15 feet wide. The combined area of the 1 window and the 1 door in her room is 60 square feet. What is the area, in square feet, of the wall surface Laura plans to paint?

2017 April(74F) Math Question 21

22. The empty container shown below is a right rectangular prism with dimensions given in inches. How many cubic inches of liquid are needed to fill the container to 75% of its capacity?

2014 April(71H) Math Question 22

2019 December(C03) Math Question 22

22. The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle, in inches?

2017 April(74F) Math Question 22

2018 December(B05) Math Question 23

2012 April(70G) Math Question 23

2010 June(68C) Math Question 23

23. The length of a rectangle is 12 feet longer than the rectangle's width. The area of the rectangle is 140 square feet. The width of the rectangle, w feet, is the positive solution to which of the following equations?

2015 December(72E) Math Question 23

23. The length of a rectangle is 4 inches longer than the width. The perimeter of the rectangle is 28 inches. What is the width of the rectangle, in inches?

2014 April(71H) Math Question 23

2009 April(66F) Math Question 24

24. The area of a certain square is 900 square inches. What is the perimeter of this square, in inches?

2021 December(E23) Math Question 24

2019 April(Z15) Math Question 25

25. The circle that has a center of (−3,4) and is tangent to the y-axis is graphed in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of this circle?

Area of Circle

Equation of a Circle

Tangent to a circle

2021 April(D05) Math Question 25

25. Matt purchased a 60-foot-long roll of chain-link fence. He used the entire roll of fence to construct a rectangular pen for his dog. Given that the pen is 12 feet wide, what is its length, in feet?

2016 December(74H) Math Question 25

2020 July(C01) Math Question 25

26. The diameter of a circle is 6 feet. What is the area, in square feet, of the circle?

2015 December(72E) Math Question 26

2018 December(B05) Math Question 26

26. The top view and side view of a 40-foot-long swimming pool are shown in the figure below. All dimensions given are in feet. The top view shows the top rectangular surface of the pool and the surrounding rectangular patio. All 4 walls of the pool are vertical and perpendicular to the top surface. The side view shows a cross section along the length of the pool. All cross sections parallel to the side view are congruent. The shallow end has a constant depth of 4 ft. The deep end has a constant depth of 9 ft. A rectangular surface connects the shallow and deep ends.

2018 June(A11) Math Question 26

2013 December(71E) Math Question 27

27. Johann put up a fence along the outer edge of the patio. Given that the materials for the fence cost $12 per foot, what was the total cost of the materials for the fence?

2018 June(A11) Math Question 27

2009 December(68A) Math Question 27

27. A rectangle is 31/-5- meters wide and 51/-S meters long.

2016 December(74H) Math Question 27

28. In rectangle ABDE shown below, C lies on BD and F lies on AE such that rectangles ABCF and CDEF are similar (ABCF — CDEF), the length of AB is 4 cm, and the length of BC is 8 cm. What is the area, in square centimeters, of ABDE ?

2014 December(72G) Math Question 28

2012 April(70G) Math Question 28

28. The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. What is the total number of white cubes that were used to build the prism?

Volume of Rectangular Prism

2021 April(Z04) Math Question 28

2013 December(71E) Math Question 29

29. One side of square ABCD has a length of 12 meters. A certain rectangle whose area is equal to the area of ABCD has a width of 8 meters. What is the length, in meters, of the rectangle?

2021 April(Z04) Math Question 29

30. Squares with sides of length x cm have been removed
from each comer of a rectangle measuring 8 cm by
18 cm, resulting in the figure shown below. In terms of
x, what is the area, in square centimeters, of the figure?

2019 June(B02) Math Question 30

2013 December(71E) Math Question 30

2012 April(70G) Math Question 30

2009 June(67C) Math Question 30

30. Ally is planting flowers around her square patio. The region she is planting is a 1-foot-wide strip that runs along 3 sides of her 5-foot-by-5-foot patio, as shown below. What is the area, in square feet, of the shaded region where Ally is planting flowers?

2021 April(D05) Math Question 30

2019 April(Z15) Math Question 31

31. The perimeter of rectangle ABCD is 96 cm. The ratio of the side lengths AB:BC is 3:5. What is the length, in centimeters, of AB ?

2015 June(73C) Math Question 31

31. A landscaper will install a triangular garden near the intersection of 2 streets. In the plan of the garden shown below, the angle nearest the intersection is a right angle. The landscaper has purchased the following materials for the garden: 1 bag of fertilizer at a price of $15.50, 50 plants at a price of $0.70 each, and 3 bags of mulch at a price of $4.00 each. An 8% sales tax was added to the total price of these materials. The landscaper will also install a water sprinkler that will be located an equal distance from the 3 vertices of the garden. The landscaper calculated the area of the garden before purchasing the fertilizer, plants, and mulch. What is the area, in square feet, of the garden?

2014 December(72G) Math Question 31

2013 December(71E) Math Question 31

31. What is the area, in square coordinate units, of this circle?

2015 April(73G) Math Question 31

31. Tomas plans to construct a circular fishpond with a diameter of 9 ft. Which of the following is closest to the length, in feet, of the decorative fencing that Tomas needs to enclose the fishpond along its perimeter?

2014 April(71H) Math Question 31

2010 December(69A) Math Question 32

2010 June(68C) Math Question 32

2010 April(68G) Math Question 32

2011 April(67F) Math Question 32

33. In the figure shown below, ABCD is a rectangle, EFGH is a square, and CD is the diameter of a semicircle. Point K is the midpoint of CD. Point J is the midpoint of both AB and EF. Points E and F lie on AB. The 3 given lengths are in meters. The length of EH is what percent of the length of AD?

Triangles, Squares, Rectangles, CirclesPerimeter, Area, VolumeACT math questions

2017 June(74C) Math Question 1

2012 December(71A) Math Question 1