6th Grade Area of Triangles and Polygons Test Solutions and Scoring (PDF)

6th Grade math test solutions: Area of Triangles and Polygons – Maths PDF

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This area polygons test answers for 6th Grade covers area of triangles and polygons (Common Core 6.G.A.1), with a free PDF to print.

Use this key to score the area test out of 20 points. Each solution is fully worked, and the scoring line explains how to award each point and partial credit.

Grade 6 · Common Core State Standards: 6.G.A.1

Area polygons test answers: worked solutions

Question 1 – Triangle [2 pts]

$\frac{1}{2} \cdot 14 \cdot 9 = 63$.

The area is $63\text{ m}^{2}$.

Scoring: 1 point for the formula; 1 point for 63.

Question 2 – Parallelogram [2 pts]

$9 \cdot 6 = 54$.

The area is $54\text{ ft}^{2}$.

Same area as a 9 by 6 rectangle.

Scoring: 1 point for the formula; 1 point for 54.

Question 3 – Trapezoid [2 pts]

$\frac{1}{2} \cdot (14 + 8) \cdot 5 = 55$.

The area is $55\text{ in}^{2}$.

Scoring: 1 point for the method (two triangles or average of the bases); 1 point for 55.

Question 4 – Find a missing dimension [2 pts]

$36 = \frac{1}{2} \cdot b \cdot 9 = 4.5b$.

$b = 36 \div 4.5 = 8$.

Scoring: 1 point for the equation; 1 point for 8 cm.

Question 5 – Composite shape [2 pts]

$12 \cdot 8 – 5 \cdot 3 = 96 – 15 = 81$.

Scoring: 1 point for the decomposition; 1 point for 81 square meters.

Question 6 – House front [2 pts]

Rectangle: $10 \cdot 6 = 60$. Triangle: $\frac{1}{2} \cdot 10 \cdot 4 = 20$.

$60 + 20 = 80$ square feet.

Scoring: 1 point for each part; 0 points for combining them incorrectly.

Question 7 – Coordinate triangle [2 pts]

Base: $7 – 1 = 6$. Height: $5 – 1 = 4$.

$\frac{1}{2} \cdot 6 \cdot 4 = 12$ square units.

Scoring: 1 point for the base and height; 1 point for 12.

Question 8 – Roof cost [3 pts]

One section: $\frac{1}{2} \cdot 20 \cdot 6 = 60$ square feet.

Both: $2 \cdot 60 = 120$ square feet.

Cost: $120 \cdot \$2.50 = \$300.00$.

Scoring: 1 point for one section; 1 point for both; 1 point for $300.00.

Question 9 – Garden plan [3 pts]

Area: $\frac{1}{2}(18 + 10) \cdot 6 = 84$ square feet.

$84 \div 14 = 6$.

She needs 6 bags.

Triangles of area 54 and 30 add to 84.

Scoring: 1 point for the area method; 1 point for 84; 1 point for 6 bags.

Total score

Total

20 points

Key facts behind this area polygons test answers

Key facts

Rectangle and parallelogram: A = bh.
Triangle: A = (1/2)bh.
Trapezoid: split into two triangles, or use A = (1/2)(b1 + b2)h.
The height is perpendicular to the base, not the slanted side.
Area is measured in square units.

How to use this area polygons test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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