Perimeter, Area, Volume

Mixed Shapes

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

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

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 April(B04) Math Question 14

2010 June(68C) Math Question 15

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

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

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

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

2020 June(C02) Math Question 23

25. Kamini is constructing the kite shown below. The kite includes 2 perpendicular supports, one of length 40 inches and the other of length 28 inches. The ends of the supports are connected with string to form a 4-sided figure that is symmetric with respect to the longer support. A layer of paper will cover the interior of the 4-sided figure. Which of the following is closest to the area, in square inches, that Kamini will cover with paper?

2018 June(A11) Math Question 25

2011 April(67F) Math Question 25

2020 June(C02) Math Question 25

2019 December(C03) Math Question 27

2010 April(68G) Math Question 27

28. The rectangular deck on Sachi's house has a width of 4 yards and a length of 6 yards. Sachi remodels the deck by increasing both the length and width by the same amount. The area of her new deck is twice the area of her original deck. What is the length, in yards, of Sachi's new deck?

2015 April(73G) Math Question 28

29. Two concentric circles have radii of 5 centimeters. and
6 centimeters, respectively. How many centimeters
longer is .the circumference of the larger circle than
that of the smaller circle?

2019 June(B02) Math Question 29

2020 July(C01) Math Question 29

30. Javier will have a pool installed in his backyard. The interior of the pool is a right circular cylinder with a uniform depth of 5 feet and a radius of 8 feet. The maximum volume of water that can be in the pool is 75% of the volume of the pool. Which of the following values is closest to the maximum number of cubic feet of water that can be in the pool?

2015 December(72E) Math Question 30

31. In the figure shown below, trapezoid ABCD is formed by AABC and AACD. The lengths are given in inches. What is the area of ABC, in square inches?

2016 April(73E) Math Question 31

32. For ABC shown below, base AC has a length of 16 inches and altitude BD has a length of 8 inches. The area of a certain square is equal to the area of ABC. What is the length, in inches, of a side of the square?

2015 June(73C) Math Question 32

32. What is the area, in square inches, of the scale drawing of the park?

2017 April(74F) Math Question 32

2019 June(72F) Math Question 35

2010 December(69A) Math Question 36

2019 June(72F) Math Question 36

2009 December(68A) Math Question 37

37. The midpoints of the sides of rectangle WXYZ are the vertices of rhombus ABCD. The dimensions of rectangle WXYZ are 6 cm by 8 cm. What is the perimeter, in centimeters, of rhombus ABCD ?

2015 December(72E) Math Question 37

2009 June(67C) Math Question 37

2020 June(C02) Math Question 37

38. The monthly rent charged for a store at Center Street Mall is $2 per square foot of floor area. The floor plan of a store at Center Street Mall is shown in the figure below, with right angles as indicated and all distances given in feet. How much monthly rent is charged for this store?

2021 June(D06) Math Question 38

2009 June(67C) Math Question 38

40. Pablo has a deck and pool in his backyard. The deck’s shape is a rectangle with a semicircle removed and is shown shaded in the figure below. The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top of the deck with stain. To decide how much stain to purchase, he needs to find the area of the top of the deck. To the nearest square foot, what is the area of the top of the deck?

2018 April(A09) Math Question 40

40. The line y = 1/2x + 3 and the line y = 3x — 12 intersect at (6,6), as shown in the standard (x,y) coordinate plane below. The shaded region is bounded by these 2 lines, the x-axis, and the y-axis. What is the area of the shaded region, in square coordinate units?

2014 December(72G) Math Question 40

2011 April(67F) Math Question 40

2019 April(B04) Math Question 41

2009 December(68A) Math Question 42

43. The circle below has a diameter of 8 centimeters. Which of the following is closest to the area, in square centimeters, of the square inscribed in the circle?

2015 April(73G) Math Question 43

2019 April(B04) Math Question 43

2011 April(67F) Math Question 43

2012 June(70C) Math Question 43

45. Toby wants to find the volume of a solid toy soldier. He fills a rectangular container 8 cm long, 6 cm wide, and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?

2017 April(74F) Math Question 45

46. A box in the shape of a cube has an interior side length of 18 inches and is used to ship a right circular cylinder with a radius of 6 inches and a height of 12 inches. The interior of the box not occupied by the cylinder is filled with packing material. Which of the following numerical expressions gives the number of cubic inches of the box filled with packing material?

2017 April(74F) Math Question 46

2012 June(70C) Math Question 47

2010 December(69A) Math Question 47

2009 April(66F) Math Question 47

2020 July(C01) Math Question 47

48. The figure shown below is composed of a rectangle and a semicircle. Points A and B are endpoints of both a side of the rectangle and a diameter of the semicircle. What is the perimeter, in feet, of the figure?

2015 April(73G) Math Question 48

49. The graph of a function y = f(x) consists of 3 line segments. The graph and the coordinates of the endpoints of the 3 line segments are shown in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of the region bounded by the graph of y .f(x), the positive y-axis, and the positive x-axis?

2017 April(74F) Math Question 49

49. In the figure below, ABCD is a trapezoid with AE perpendicular to AB; AE is 10 units long; and DC is 28 units long. If the area of right triangle LEBA is 60 square units, what is the area, in square units, of trapezoid ABCD ?

2016 December(74H) Math Question 49

2020 June(C02) Math Question 49

2010 June(68C) Math Question 50

51. Circles with centers A, B, and C, respectively, are mutually tangent, as shown below, and have radii of lengths a, b, and c, respectively. The lengths of AB, BC, and AC are 13 inches, 15 inches, and 26 inches, respectively. What is the value of a + b + c ?
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2013 June(71C) Math Question 51

55. In the diagram below, B, F, and H are on AC, AE, and BF, respectively, and GH I BE. The area of square ABGF is -12-t the area of square ACDE. What percent of the area of ACDE does the shaded portion represent?

Mixed ShapesPerimeter, Area, VolumeACT math questions

2013 June(71C) Math Question 7

2019 June(B02) Math Question 10