ARKTIK EDUCATION

See the court. Prove the geometry.

GEM-12 · Geometry · 25 minutes

Use area, perimeter, scale and the Pythagorean theorem with correct units.

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Diagnose · 0–5 minutes

  1. What is the difference between the floor inside a court and the boundary around it?
  2. Why does area use square units?
  3. Which side is the hypotenuse of a right triangle?

Teach · 5–10 minutes

An NBA court is 94 feet long and 50 feet wide inside its boundaries. Painting the playing surface concerns area: 94 x 50 = 4,700 square feet. Measuring the boundary concerns perimeter: 2 x (94 + 50) = 288 feet. A school or community court can have different dimensions; measure or check its own diagram rather than assuming NBA dimensions.

Draw the NBA court at one inch for every ten feet. Divide both real dimensions by 10: 9.4 inches by 5 inches. The perimeter shrinks by a factor of 10, while the area shrinks by a factor of 100. Always label drawing inches separately from real feet.

A diagonal is the hypotenuse of a right triangle with legs 94 and 50 feet. Its length is the square root of 94 squared plus 50 squared: about 106.47 feet. It is longer than either side and shorter than walking along both sides (144 feet). A rectangular corner is 90 degrees. A triangle's three interior angles total 180 degrees.

NBA court rectangle and diagonalA rectangle 94 feet long and 50 feet wide. A diagonal connects opposite corners. Diagram is for geometry, not a complete court marking plan.94 feet50 feetdiagonal ≈ 106.5 feet
Find the boundary, surface and diagonal. They answer different questions and use different units.

Practice · 10–15 minutes

Draw and label the scaled court. Mark a diagonal and both legs. Explain which measurement would be useful to a painter and which to someone installing a boundary strip.

Prove · 15–23 minutes

Use new questions without notes or hints. Record assistance honestly. All questions must be answered before checking.

1. NBA playing-surface area is:
2. NBA boundary perimeter is:
3. At one inch per ten feet, the court drawing is:
4. Which calculation finds the diagonal?
5. If one triangle angle is 90 degrees and another is 35 degrees, the third is:

Correct · 23–25 minutes

For each missed answer, name the concept, show the evidence or calculation and explain why your first reasoning failed. Score alone does not authorize advancement.

Adult review and delayed check

Target: at least 4/5 practice questions plus an explanation earning at least 2/3 rubric points: accurate claim, relevant evidence, clear reasoning (one point each). An adult decides whether the explanation is acceptable. Repeat a different five-question check after 48–72 hours, independently, with at least 4/5. This ARKTIK instructional target is not an official AP standard.

Delayed check questions — use after 48–72 hours
  1. A half-length NBA court rectangle is 47 by 50 feet. Its area is:
    • 2,350 square feet
    • 194 square feet
    • 4,700 square feet
  2. Its perimeter is:
    • 97 feet
    • 194 feet
    • 2,350 feet
  3. Doubling every side length multiplies area by:
    • 2
    • 4
    • 8
  4. A right triangle has legs 3 and 4 units. Its hypotenuse is:
    • 5 units
    • 7 units
    • 12 units
  5. The area of a triangle with base 10 and perpendicular height 6 is:
    • 60 square units
    • 30 square units
    • 16 units

Adult coach answers are in the separate coach guide. Keep it closed during assessment.

Sources and scope

Original ARKTIK practice, prepared with AI assistance and checked for factual and scoring consistency. Review teacher materials for the current unit; these three missions are not a complete course or a completed TEKS alignment.