← Back to the Area Of Polygons test
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Award the points in each scoring line. Accept any valid decomposition of a composite figure. Give full credit for a correct answer with work shown, and take off the units point when square units are missing.
Standards: 6.G.A.1 · Level: Grade 6
Question 1 Triangle and parallelogram (2 points)
- 12 × 13 × 8 = 52, so 52 square feet.
- 14 × 6.5 = 91, so 91 square meters.
Scoring: 1 point for each part.
Question 2 Area of a trapezoid (2 points)
A = 12 (9 + 15) × 5 = 12 × 5 = 60.
60 square inches
Scoring: 1 point for a correct setup, 1 point for the answer with units.
Question 3 Missing height (2 points)
65 = 12 × 10 × h = 5h, so h = 65 ÷ 5 = 13.
13 feet
Scoring: 1 point for the equation, 1 point for the answer.
Question 4 Composite floor plan (3 points)
Split the floor into a 16 by 5 rectangle and a 9 by 4 rectangle. 80 + 36 = 116. Check: 16 × 9 − 7 × 4 = 144 − 28 = 116.
116 square feet
Scoring: 1 point for a valid decomposition or missing side, 1 point for the two areas, 1 point for the total with units.
Question 5 Playground shade (3 points)
- 12 × 12 × 9 = 54 square feet.
- 7 × 5 = 35 square feet.
- 54 − 35 = 19 square feet.
Scoring: 1 point for each part.
Question 6 Mural wall (3 points)
- 12 (20 + 14) × 9 = 17 × 9 = 153 square feet.
- 153 ÷ 36 = 4.25, so 4 quarts are not enough: 5 quarts.
Scoring: 2 points for part (a) (1 for the setup); 1 point for rounding up to 5.
Question 7 Comparing two shapes (3 points)
- Shape A: 16 × 9 = 144 square inches. Shape B: 12 × 24 × 12 = 144 square inches.
- The two areas are equal.
Scoring: 1 point for each area; 1 point for the comparison.
Question 8 Missing base (2 points)
156 = b × 12, so b = 156 ÷ 12 = 13.
13 meters
Scoring: 1 point for the equation, 1 point for the answer.