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. A circle has diameter 14. What is its circumference?

A) 28π

B) 7π

C) 49π

D) 14π

Explanation: Circumference = πd = 14π

2 / 27

2. What is the perimeter of a square with side 9?

A) 18

B) 27

C) 36

D) 45

Perimeter = 4s = 4 × 9 = 36.

3 / 27

3. A cylinder has volume 192π and radius 4. What is its height?

A) 8

B) 6

C) 12

D) 10

π(16)h=192π. h=12.

4 / 27

4. What is the distance from the origin to the point (5, 12)?

A) 7

B) 17

C) 13

D) 15

d = √(5²+12²) = √(25+144) = √169 = 13.

5 / 27

5. Two triangles are congruent. Their perimeters are 24 and x. What is x?

A) 48

B) Cannot determine

C) 12

D) 24

Congruent triangles have equal perimeters. x=24.

6 / 27

6. A chord in a circle subtends a 90° angle at the center. If radius is 5, what is the chord length?

A) 5√2

B) 5

C) 10

D) √10

Chord=r√2=5√2 (45-45-90).

7 / 27

7. A square is inscribed in a circle of radius 5. What is the side of the square?

A) 10

B) 5/√2

C) 5√2

D) 5

Diagonal=2r=10. Side=10/√2=5√2.

8 / 27

8. What is the diagonal of a rectangular prism 3×4×5?

A) √52

B) √50

C) √54

D) √53

d=√(9+16+25)=√50=5√2.

9 / 27

9. Two angles of a quadrilateral are 90° each. The other two are equal. What are they?

A) 120°

B) 60°

C) 90°

D) 180°

360-90-90=180. Two equal angles: 180/2=90°.

10 / 27

10. What is the area of a triangle with sides 6, 8, 10?

A) 48

B) 12

C) 24

D) 30

It's a right triangle (6²+8²=10²). A=½×6×8=24.

11 / 27

11. What is the volume of a pyramid with triangular base area 24 and height 9?

A) 72

B) 216

C) 36

D) 108

V=⅓×24×9=72.

12 / 27

12. In a right triangle, the altitude to the hypotenuse creates two smaller triangles. These triangles are:

A) Equal in area

B) Similar to each other and to the original

C) None of these

D) Congruent to each other

Both smaller triangles are similar to each other and to the original right triangle.

13 / 27

13. If the perimeter of a square equals the circumference of a circle, and the square has side 5, what is the circle's radius?

A) 5π

B) 10/π

C) 20/π

D) 5/π

Square P=20. Circle C=20. 2πr=20. r=10/π.

14 / 27

14. A rectangular box has dimensions 2×3×4. What is the length of the space diagonal?

A) √27

B) √24

C) √53

D) √29

d=√(4+9+16)=√29.

15 / 27

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

A) 150

B) 100

C) 200

D) 125

SA = 6s² = 6 × 25 = 150.

16 / 27

16. What is the measure of each interior angle of a regular octagon?

A) 150°

B) 125°

C) 135°

D) 120°

(8-2)×180/8=1080/8=135°.

17 / 27

17. What is the area of a parallelogram with base 8 and height 5?

A) 30

B) 20

C) 40

D) 45

A = base × height = 8 × 5 = 40.

18 / 27

18. A cone has diameter 8 and height 6. What is its volume?

A) 96π

B) 48π

C) 64π

D) 32π

r=4. V=⅓π(16)(6)=32π.

19 / 27

19. What is the measure of the angle formed by a tangent and a chord at the point of tangency if the arc is 110°?

A) 55°

B) 110°

C) 220°

D) 70°

Tangent-chord angle=½ arc=55°.

20 / 27

20. What is the perimeter of a right triangle with legs 6 and 8?

A) 32

B) 30

C) 28

D) 24

Hypotenuse = √(36+64) = 10. P = 6+8+10 = 24.

21 / 27

21. If two lines have slopes 2 and -1/2, they are:

A) Neither

B) Parallel

C) Equal

D) Perpendicular

m₁×m₂=2×(-1/2)=-1. Perpendicular.

22 / 27

22. A triangle has two sides 8 and 15 and the included angle is 90°. What is its area?

A) 30

B) 45

C) 120

D) 60

A=½×8×15=60.

23 / 27

23. A regular polygon has interior angles of 150°. How many sides does it have?

A) 15

B) 10

C) 20

D) 12

(n-2)×180/n = 150 → 180n-360=150n → 30n=360 → n=12.

24 / 27

24. A sphere's radius doubles. By what factor does its volume change?

A) 6

B) 8

C) 4

D) 2

V=⅔πr³. If r doubles: V increases by 2³=8.

25 / 27

25. A circle has area 64π. What is its circumference?

A) 16π

B) 64π

C) 8π

D) 32π

r²=64→r=8. C=2π(8)=16π.

26 / 27

26. What is the sum of interior angles of a decagon (10 sides)?

A) 720°

B) 1440°

C) 1800°

D) 1080°

(10-2) × 180° = 8 × 180° = 1440°.

27 / 27

27. 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).

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