ACT Geometry Practice Questions with Answers
Geometry questions reward a clean picture and the right formula. Sketch each one before you solve.
These questions were written by NextPoint in the style of the ACT and are not from an official test. The formulas used are listed in ACT Math formulas to memorize.
A circle has an area of 49π. What is its circumference?
- A. 7π
- B. 28π
- C. 14π
- D. 49π
- E. 98π
Show answer and solution
Answer: C. Area = πr² = 49π, so r² = 49 and r = 7. Circumference = 2πr = 2π(7) = 14π.
A rectangle has a perimeter of 36, and its length is twice its width. What is its area?
- A. 48
- B. 72
- C. 54
- D. 64
- E. 81
Show answer and solution
Answer: B. Let the width be w and the length 2w. Perimeter = 2(w + 2w) = 6w = 36, so w = 6 and the length is 12. Area = 6 × 12 = 72.
What is the measure of each interior angle of a regular hexagon?
- A. 100°
- B. 108°
- C. 135°
- D. 144°
- E. 120°
Show answer and solution
Answer: E. The interior angles of a hexagon add up to (6 − 2) × 180° = 720°. A regular hexagon has 6 equal angles, so each is 720° ÷ 6 = 120°.
Triangle A has sides 3, 4 and 5. Triangle B is similar to Triangle A, and its hypotenuse is 15. What is the area of Triangle B?
- A. 18
- B. 36
- C. 45
- D. 54
- E. 90
Show answer and solution
Answer: D. The hypotenuse grew from 5 to 15, a scale factor of 3, so Triangle B has legs 9 and 12. Its area is ½ × 9 × 12 = 54. Do not multiply the area of Triangle A (6) by 3: areas scale by the factor squared, 6 × 9 = 54.
Geometry habits that save points
- Write down each given number on your sketch before you start.
- Check what is asked: perimeter or area, radius or diameter, one angle or the sum.
- For similar figures, lengths scale by the factor, areas by the factor squared and volumes by the factor cubed.
Keep going with ACT Math tips and tricks.
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