Geometry Test PDF
Free preview of a printable Geometry test with a complete step-by-step answer key. Common Core HSG aligned · balanced 5/3/2 difficulty.
1. A triangle has angles 50° and 60°. Find the third angle.
2. Find the area of a rectangle 8 cm by 5 cm.
3. Find the perimeter of a square with side 7 cm.
4. Find the circumference of a circle with radius 5 cm. Use π ≈ 3.14.
5. Two angles are complementary. One is 35°. Find the other.
6. Right triangle: legs 6 and 8. Find the hypotenuse.
7. Find the area of a triangle with base 12 cm and height 9 cm.
8. Find the area of a circle with diameter 10 cm. Use π ≈ 3.14.
9. Triangle ABC: AB = 9, BC = 12, angle B = 90°. Find AC.
10. A cylinder has radius 3 and height 10. Find the volume. Use π ≈ 3.14.
1. 70°
180 − (50 + 60) = 70°
2. 40 cm²
A = l × w = 8 × 5 = 40
3. 28 cm
P = 4s = 4 × 7 = 28
4. 31.4 cm
C = 2πr = 2(3.14)(5) = 31.4
5. 55°
90 − 35 = 55°
6. 10
c² = 6² + 8² = 36 + 64 = 100 → c = 10
7. 54 cm²
A = (1/2)bh = (1/2)(12)(9) = 54
8. 78.5 cm²
r = 5; A = πr² = 3.14(25) = 78.5
9. 15
AC² = 9² + 12² = 81 + 144 = 225 → AC = 15
10. 282.6
V = πr²h = 3.14(9)(10) = 282.6
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Topics covered
Triangles, angles, area, perimeter, Pythagorean theorem, circles, volume.
Difficulty balance
5 easy / 3 medium / 2 hard — fair grading across abilities.
Answer key
Step-by-step solutions with full working.