Training Geometry Placement Test Practice — Geometry
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Placement Test Practice — Geometry

25 min Geometry

Placement Test Practice — Geometry

This practice test covers the full range of geometry topics from this module — angles, triangles, perimeter, area, surface area, volume, and coordinate geometry. It is designed to mirror the style and difficulty of a placement test.

Work through the problems under timed conditions, then check your answers and review any topics where you struggled.

These problems cover geometry topics commonly tested on college math placement exams.

Practice Test — 25 Questions

1. Find the area of a triangle with base 20 and height 13.
2. A circle has radius 8. Find the area.
3. A right triangle has legs 5 and 12. Find the hypotenuse.
4. Find the circumference of a circle with diameter 14.
5. Volume of a rectangular box: $l=9$, $w=4$, $h=5$.
6. Find the supplement of $73°$.
7. Distance between $(2, -3)$ and $(7, 9)$.
8. Area of a trapezoid with bases 12 and 20, height 8.
9. Volume of a cylinder: $r=7$, $h=10$.
10. Midpoint of $(-1, 5)$ and $(3, -7)$.
11. A square has area 196. Find the side length and perimeter.
12. Surface area of a sphere with $r=3$.
13. A right triangle has hypotenuse 25 and one leg 7. Find the other.
14. Slope of line through $(0, -4)$ and $(6, 8)$.
15. Volume of a cone: $r=5$, $h=15$.
16. Find the complement of $58°$.
17. Is a triangle with sides 9, 40, 41 a right triangle?
18. Area of a circle with circumference $10\pi$.
19. A box has $SA=150$ and is a cube. Find $s$.
20. A parallelogram has base 18 and height 7. Find the area.
21. Find the diagonal of a rectangle: $l=8$, $w=15$.
22. Volume of a hemisphere: $r=6$.
23. The angles of a triangle are $x$, $2x$, and $3x$. Find them.
24. A sector has $r=12$ and central angle $60°$. Find the area.
25. Center and radius of $(x+1)^2 + (y-4)^2 = 36$.
Show Answer Key

1. $130$

2. $64\pi \approx 201.06$

3. $13$

4. $14\pi \approx 43.98$

5. $180$

6. $107°$

7. $\sqrt{25 + 144} = 13$

8. $128$

9. $490\pi \approx 1{,}539.38$

10. $(1, -1)$

11. $s = 14$; $P = 56$

12. $36\pi \approx 113.10$

13. $24$

14. $2$

15. $125\pi \approx 392.70$

16. $32°$

17. $81 + 1600 = 1681 = 41^2$ ✓ Yes

18. $C = 2\pi r = 10\pi \implies r = 5$; $A = 25\pi$

19. $6s^2 = 150 \implies s = 5$

20. $126$

21. $17$

22. $\frac{2}{3}\pi(216) = 144\pi \approx 452.39$

23. $6x = 180 \implies x = 30°$. Angles: $30°, 60°, 90°$.

24. $60° = \frac{\pi}{3}$; $A = \frac{1}{2}(144)\frac{\pi}{3} = 24\pi \approx 75.40$

25. Center $(-1, 4)$, radius $6$

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