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Polygons on the Coordinate Plane — 6th Math: Geometry practice questions

31 multiple-choice questions and 20 flashcards on Polygons on the Coordinate Plane, about 21% of the 6th Math: Geometry bank. Every one carries a written rationale.

Written and maintained by Nick Burton · last updated 2026-08-22 · how we write and review questions

What this chapter covers

Polygons on the Coordinate Plane is one of 4 chapters in CoStudy's 6th Math: Geometry bank, and it holds 31 of the bank's 150 multiple-choice questions — roughly 21% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Polygons on the Coordinate Plane practice questions

10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

A square has vertices (−3, 0), (−3, 4), (1, 4), (1, 0). Its perimeter:

  1. 8
  2. 12
  3. 16
  4. 20

Answer: C — 16

C) Side 4 → P = 16. A) Two sides. B) Three sides. D) Used 5 sides.

A trapezoid with parallel sides 6 and 10 and height 4 has area:

  1. 32
  2. 24
  3. 40
  4. 20

Answer: A — 32

A = (1/2)(b₁+b₂)h = (1/2)(16)(4) = 32. (B), (C), (D) miscalculate.

Perimeter of a rectangle with vertices (0, 0), (6, 0), (6, 4), (0, 4):

  1. 10
  2. 20
  3. 24
  4. 14

Answer: B — 20

B) P = 2(6 + 4) = 20. A) Used just one length + one width. C) Computed the area. D) Used 6 + 4 + 4 only.

A polygon has vertices on the coordinate plane. To find its perimeter:

  1. Use any random formula
  2. Find the distance between each pair of consecutive vertices and sum them (for horizontal/vertical sides, use coordinate differences)
  3. Use only the first side
  4. Multiply x by y

Answer: B — Find the distance between each pair of consecutive vertices and sum them (for horizontal/vertical sides, use coordinate differences)

Perimeter sums side lengths. (A), (C), (D) misread.

A right triangle has legs 5 and 12. Its area is:

  1. 17
  2. 13
  3. 60
  4. 30

Answer: D — 30

A = (1/2)(5)(12) = 30. (A) adds legs; (C) doesn't halve; (B) is hypotenuse.

A triangle has base 12 and area 30. Its height is:

  1. 2.5
  2. 5
  3. 10
  4. 18

Answer: B — 5

30 = (1/2)(12)(h) → 30 = 6h → h = 5. (A), (C), (D) miscalculate.

A right triangle has vertices (2, 1), (2, 7), (6, 1). Its area:

  1. 12
  2. 24
  3. 18
  4. 6

Answer: A — 12

A) Legs |7−1|=6 and |6−2|=4 → ½(6)(4) = 12. B) Forgot ½. C) Used 6 alone. D) Halved wrong.

A rectangle has vertices (1, 1), (1, 5), (4, 5), (4, 1). What is its area?

  1. 7
  2. 12
  3. 15
  4. 20

Answer: B — 12

Width = 4−1 = 3. Height = 5−1 = 4. Area = 12. (A) adds; (C), (D) miscalculate.

On a coordinate plane, the distance from (2, 3) to (2, 9) is:

  1. 3
  2. 6
  3. 9
  4. 12

Answer: B — 6

Same x: |9−3| = 6. (A), (C), (D) miscalculate.

Three vertices of a rectangle are (0, 0), (8, 0), and (0, 5). The fourth is:

  1. (5, 8)
  2. (8, 0)
  3. (4, 2.5)
  4. (8, 5)

Answer: D — (8, 5)

D) Opposite (0,0): (8, 5). A) Swapped coords. C) Center. B) Repeated a given vertex.

Polygons on the Coordinate Plane flashcards

4 cards from the 20 in this chapter.

What is the area of a regular hexagon — easy way?

Divide into 6 equilateral triangles. Compute area of one and multiply by 6.

In a triangle, what are 'base' and 'height'?

Base = any side. Height = perpendicular distance from base to opposite vertex.

What is a rhombus?

Parallelogram with all sides equal.

What polygon has 8 sides?

Octagon.

Practise the full chapter

These are a sample. The full Polygons on the Coordinate Plane chapter runs 51 items with per-chapter progress tracking, on the web and in the iOS app.

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