Perimeter, Area, Volume

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

Tisha is building a wooden drying rack. The top of the rack is in the shape of a trapezoid. The trapezoid's bases are 24 inches long and 38 inches long, respectively. Tisha will add a brace that joins the midpoints of the trapezoid's 2 nonparallel sides to support her drying rack, as shown in the figure below. How many inches long will the brace be?

2023 September(G01) 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

A certain rectangle has a width of 6 km and a length that is 4 km more than 2 times the width. What is the area, in square kilometers, of this rectangle?

2024 April(Z13) 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

2019 June(72F) Math Question 5

5. When Tyrese fell asleep one night, the temperature was 24°F. When Tyrese awoke the next morning, the temperature was —16°F. Letting + denote a rise in temperature and — denote a drop in temperature, what was the change in temperature from the time Tyrese fell asleep until the time he awoke?

2017 December(A10) Math Question 5

5. A formula for the volume of a right circular cone is

2017 June(74C) Math Question 5

2012 June(70C) Math Question 5

A rectangular field measures 300 feet by 200 feet. A rectangular portion of the field measuring 225 feet by 175 feet is paved for a parking lot, and the rest of the field is left unpaved. How many square feet of the field are left unpaved?

2024 December(H31) Math Question 5

2009 April(66F) Math Question 6

2009 December(68A) Math Question 7

7. A square and a rectangle have the same area. The length of the rectangle is 32 centimeters, and the width of the rectangle is 2 centimeters. What is the length, in centimeters, of a side of the square?

2013 June(71C) Math Question 7

What is the volume, in cubic inches, of a sphere with a diameter of 10 inches? (Note: The volume, V, of a sphere with radius r is given by the formula V = (4/3)πr³.)

2023 April(F11) Math Question 9

2020 July(C01) Math Question 10

10; Iv.th e figure below, a circle with a radius of i O meters
circumscribes a regular hexagon. What is the perimeter,
in meters, of the hexagon?

2019 June(B02) Math Question 10

2009 June(67C) 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

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. At her hot dog stand, Julie sells hot dogs for $2 each. Purchasing hot dogs and other supplies costs $200 per month. The solution of which of the following inequalities models the numbers of hot dogs, h, Julie can sell per month and make a profit?

2017 December(A10) 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

A rectangular field that measures 300 meters by 175 meters is to be completely fenced along its perimeter. Given that fencing sells for $2.05 per meter, what will the fencing for the field cost?

2024 June(G20) 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

12. Square ABEF and parallelogram ACDG are shown in the figure below. Points •E and F are on DG, B is on AC, and the lengths given are in inches. What is the ratio of the area of ABEF to the area of ACDG ?

2013 June(71C) 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

The dimensions of a hallway floor are shown below. Each pair of adjacent walls meets at a right angle. Teresa plans to completely carpet this entire hallway floor. At a cost of $2 per square foot, how much will carpeting this hallway floor cost?

2023 September(G01) 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

14. The volume of a sphere is 41c3r , where r is the radius
of the sphere. What is the volume, in cubic yards, of a sphere with a diameter of 4 yards?

2018 June(A11) Math Question 14

2009 April(66F) Math Question 14

2019 April(B04) Math Question 14

2013 December(71E) Math Question 14

2020 June(C02) Math Question 14

14. An ellipse with a major axis of length 6 inches and a minor axis of length 4 inches is inscribed in a rectangle, as shown below. The region inside the rectangle but outside the ellipse is shaded. What is the area, in square inches, of the shaded region? (Note: The area, A, of any ellipse can be found by the formula A = πab where a is the length of the major axis and b is the length of the minor axis.)

Area of Ellipse

2020 December(D03) Math Question 14

2013 April(71G) Math Question 15

2011 June(69F) 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

15. In the figure below, all of the small squares are equal in area, and the area of rectangle ABCD is 1 square unit. Which of the following expressions represents the area, in square units, of the shaded region?

2016 December(74H) Math Question 15

2012 April(70G) Math Question 15

2010 June(68C) 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 perimeter of a parallelogram is 80 inches, and the length of 1 side is 16 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

2015 December(72E) Math Question 16

16. Marcie will paint the shaded region (1 pentagonal wall) of the outside of the playhouse shown below. All given dimensions are in feet. Each 1-quart container of paint will cover 50 square feet, and only 1 coat of paint will be applied. How many 1-quart containers of paint will Marcie need in order to cover the 1 pentagonal wall of the playhouse?

2015 April(73G) 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

Each side of square ABCD has a length of 20 ft. A certain rectangle whose area is equal to the area of ABCD has a width of 10 ft. What is the length, in feet, of the rectangle?

2023 April(F11) Math Question 16

The circular region containing the track and the infield (the grassy region enclosed by the track) is divided into sectors that each have a central angle of 60°. Each sector is a different color. What is the area, in square meters, of each sector?

35 February(Z14) Math Question 16

The following shapes are a circle and some regular polygons that have their centers marked. All units are given in feet. Which of these shapes has the greatest area?

2024 April(Z13) Math Question 16

17. Tina runs at a rate of 8 miles per hour. At that rate, how many miles will she run in 12 minutes?

2017 December(A10) Math Question 17

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 June(67C) Math Question 17

17. In the figure below, all of the small squares are equal in area, and the area of rectangle ABCD is 1 square unit. Which of the following expressions represents the area, in square units, of the shaded region?

2016 April(73E) Math Question 17

The isosceles triangle shown below has congruent legs that are each 10 centimeters long. The perimeter of the triangle is 32 centimeters. What is the length, in centimeters, of the altitude that splits the triangle into 2 congruent right triangles?

2024 June(G20) Math Question 17

18. The rectangle shown• in the figure below is partitioned into 3 triangles, 2 of which are shaded. What is the total area, in square inches, of the 2 shaded regions?

2017 June(74C) Math Question 18

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

The area of the trapezoid shown below is 20 square feet, the height is 5 feet, and the length of one base is 2 feet. What is b, the length of the other base, in feet?

35 February(Z14) 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

19. A scale drawing of Corinne’s bedroom floor is shown below. All given dimensions are in feet, and all intersecting line segments shown are perpendicular. Corinne wants to completely cover the floor with square hardwood tiles. Each tile has a side length of 1 foot, and no tiles will be cut. How many tiles will Corinne need to cover the floor?

2016 December(74H) Math Question 19

2009 December(68A) Math Question 19

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?

35 February(Z14) Math Question 19

Which of the following equations expresses a relationship between D, the length of the diagonal of the square shown below, and S, the length of a side of the square?

2023 September(G01) 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. Marcos programs his calculator to evaluate a linear function, but he doesn't say what the function is. When 5 is entered, the calculator displays the value 2. When 15 is entered, the calculator displays the value 6. Which of the following expressions explains what the calculator will display when any number, n, is entered?

2017 December(A10) Math Question 20

20. The perimeter of a parallelogram is 80 inches, and the length of 1 side is 18 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

2014 April(71H) 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

20. In the figure below, all segments that meet do so at right angles. What is the area, in square units, of the shaded region?

2018 June(A11) Math Question 20

2011 June(69F) Math Question 20

2009 June(67C) Math Question 20

21. On Friday, the temperature at 8:00 a.m. was 49°F and rose at a constant rate of °F per hour until noon. A cold front passed through at noon, and the temperature then fell at a constant rate of 1°F per hour. The temperature first fell below 49°F between:

2017 December(A10) Math Question 21

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

In the figure shown, a square is circumscribed about a circle with an 8-inch radius. Diameter AB is parallel to 2 sides of the square, and CD is a diagonal of the square. Some regions, bounded by the square, the circle, AB, and CD, are shaded. Which of the following is closest to the total area, in square inches, of the shaded regions?

2025 October(J08) 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?

Perimeter, Area, VolumeThere are 355 ACT math questions under Perimeter, Area, Volume

Sub-topics

2017 June(74C) Math Question 1

2012 December(71A) Math Question 1