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Math · Plane Geometry

Hard Plane Geometry Drill

15 hard-difficulty ACT Math questions on Plane Geometry. Each question is on its own page with a worked answer explanation, the underlying rule, and a quick study tip.

Hard Math Plane Geometry

All 15 questions

  1. 1 Area of a Triangle A triangle has base 12 cm and height 9 cm. What is its area in square centimeters? Hard
  2. 2 Area of a Circle What is the area of a circle with radius 3? Express your answer in terms of π. Hard
  3. 3 Pythagorean Theorem A right triangle has legs of length 6 and 8. What is the length of its hypotenuse? Hard
  4. 4 Perimeter of a Rectangle A rectangle has length 5 and width 3. What is its perimeter? Hard
  5. 5 Area of a Triangle A triangle has base 12 cm and height 7 cm. What is its area in square centimeters? Hard
  6. 6 Area of a Circle What is the area of a circle with radius 6? Express your answer in terms of π. Hard
  7. 7 Pythagorean Theorem A right triangle has legs of length 6 and 8. What is the length of its hypotenuse? Hard
  8. 8 Perimeter of a Rectangle A rectangle has length 7 and width 6. What is its perimeter? Hard
  9. 9 Area of a Triangle A triangle has base 10 cm and height 5 cm. What is its area in square centimeters? Hard
  10. 10 Area of a Circle What is the area of a circle with radius 6? Express your answer in terms of π. Hard
  11. 11 Pythagorean Theorem A right triangle has legs of length 5 and 12. What is the length of its hypotenuse? Hard
  12. 12 Perimeter of a Rectangle A rectangle has length 9 and width 3. What is its perimeter? Hard
  13. 13 Area of a Triangle A triangle has base 12 cm and height 9 cm. What is its area in square centimeters? Hard
  14. 14 Area of a Circle What is the area of a circle with radius 3? Express your answer in terms of π. Hard
  15. 15 Pythagorean Theorem A right triangle has legs of length 5 and 12. What is the length of its hypotenuse? Hard

How to use this drill

Open the questions one at a time. Read the prompt, decide on an answer before scrolling, then check the explanation. The point of a drill is not to "get the question right" — it's to internalize the rule so you can apply it cold under timed conditions on test day.

If you're missing more than a third of the questions in this set, drop down a difficulty tier and rebuild from there. If you're getting all of them quickly, jump up a tier and try a mixed drill across subtopics.

What "Hard" means here

Hard questions are designed to separate strong test-takers. They typically require multiple rules applied in sequence, or careful elimination among answers that all look plausible. Expect to see these appear later in real ACT sections; even strong test-takers miss a couple per test.

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