Enhance Your Skills with Our ACT Geometry Practice Test/Quiz

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30 random questions |30 minutes | Questions are randomized every attempt. Good luck!

ACT Math - Geometry Practice Test

Test your ACT geometry skills with 30 random practice test questions covering shapes, angles, and measurements!

1 / 27

1. What is the sum of all angles in a hexagon?

A) 900°

B) 540°

C) 720°

D) 1080°

(6-2)×180=720°.

2 / 27

2. A rectangular prism has length 10, width 4, height 3. What is its surface area?

A) 164

B) 184

C) 104

D) 144

SA = 2(lw+lh+wh) = 2(40+30+12) = 2(82) = 164.

3 / 27

3. What is the volume of a pyramid with square base side 6 and height 4?

A) 48

B) 24

C) 96

D) 72

V=⅓×36×4=48.

4 / 27

4. What is the area of a right triangle with hypotenuse 10 and one angle 30°?

A) 25

B) 12.5

C) 25√3/2

D) 50

Legs: 5 and 5√3. A=½×5×5√3=25√3/2.

5 / 27

5. In a right triangle, if one acute angle is 25°, what is the other?

A) 65°

B) 55°

C) 85°

D) 75°

90°-25°=65°.

6 / 27

6. A sphere has radius 6. What is its surface area?

A) 144π

B) 72π

C) 108π

D) 36π

SA=4πr²=4π(36)=144π.

7 / 27

7. A cylinder has diameter 6 and height 10. What is its volume?

A) 360π

B) 45π

C) 90π

D) 180π

r=3. V=π(9)(10)=90π.

8 / 27

8. What is the equation of a line through (0,0) with slope -2?

A) y=-2x+1

B) y=2x

C) y=-2x

D) y=-2

y=mx+b. m=-2, b=0. y=-2x.

9 / 27

9. What is the measure of the angle at the center of a regular decagon?

A) 30°

B) 36°

C) 45°

D) 72°

360°/10=36°.

10 / 27

10. Two angles in a triangle are 55° and 75°. What is the third?

A) 70°

B) 60°

C) 40°

D) 50°

180-55-75=50°.

11 / 27

11. What is the perimeter of a regular pentagon with side 8?

A) 56

B) 40

C) 48

D) 32

P = 5 × 8 = 40.

12 / 27

12. What is the area of a trapezoid with bases 6 and 10 and height 4?

A) 40

B) 48

C) 24

D) 32

A = ½(b₁+b₂)h = ½(16)(4) = 32.

13 / 27

13. A circle has circumference 16π. What is its radius?

A) 6

B) 8

C) 4

D) 16

C = 2πr = 16π → r = 8.

14 / 27

14. What is the measure of each exterior angle of a regular pentagon?

A) 60°

B) 72°

C) 90°

D) 108°

Each exterior angle = 360°/n = 360°/5 = 72°.

15 / 27

15. A right triangle has legs 3 and 4. What is the hypotenuse?

A) 6

B) 7

C) 5

D) 25

Explanation: c² = 3² + 4² = 9 + 16 = 25, so c = 5

16 / 27

16. What is the perimeter of a rhombus with diagonals 6 and 8?

A) 28

B) 40

C) 20

D) 24

Side=√(3²+4²)=5. P=4×5=20.

17 / 27

17. What is the area of a sector with radius 6 and central angle 90°?

A) 6π

B) 9π

C) 12π

D) 18π

Area = (90/360)πr² = (1/4)π(36) = 9π.

18 / 27

18. What is the area of a triangle with vertices (0,0), (6,0), (3,4)?

A) 16

B) 12

C) 14

D) 10

A = ½ × base × height = ½ × 6 × 4 = 12.

19 / 27

19. What is the coordinate of the centroid of a triangle with vertices (0,0), (6,0), (0,9)?

A) (2,4.5)

B) (3,4.5)

C) (2,3)

D) (3,3)

Centroid=((0+6+0)/3,(0+0+9)/3)=(2,3).

20 / 27

20. What is the surface area of a cube with side 5?

A) 100

B) 125

C) 150

D) 200

SA = 6s² = 6 × 25 = 150.

21 / 27

21. What is the area of a sector with r=5 and θ=2 radians?

A) 25

B) 10

C) 5

D) 50

A=½r²θ=½(25)(2)=25.

22 / 27

22. What is the perimeter of a sector with r=6 and central angle 120°?

A) 12π+6

B) 4π+12

C) 4π+6

D) 6π+12

Arc=(120/360)(2π×6)=4π. P=4π+6+6=4π+12.

23 / 27

23. What is the volume of a hemisphere with radius 6?

A) 144π

B) 288π

C) 216π

D) 72π

V=⅔πr³=⅔π(216)=144π.

24 / 27

24. A cone has radius 5 and slant height 13. What is its height?

A) 10

B) 11

C) 12

D) 14

h=√(13²-5²)=√(169-25)=√144=12.

25 / 27

25. What is the area of a circle with radius 10?

A) 100π

B) 20π

C) 1000π

D) 10π

A=πr²=100π.

26 / 27

26. What is the center of the circle (x+3)²+(y-2)²=16?

A) (-3, 2)

B) (3, -2)

C) (3, 2)

D) (-3, -2)

Center at (h,k)=(-3, 2).

27 / 27

27. Two complementary angles have a difference of 18°. What are they?

A) 40° and 50°

B) 45° and 45°

C) 36° and 54°

D) 54° and 36°

x+(x+18)=90. 2x=72. x=36, other=54.

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