Area of polygons worksheet

Grade 6 math, Common Core 6.G.A.1. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Area of polygons

Grade 6 math, Common Core 6.G.A.1

Find the area of each shape. Include the units.

1.
A parallelogram has a base of 4 cm and a height of 5 cm.
2.
A house shape is a rectangle 10 m wide and 9 m tall, with a triangle roof on top that has the same 10 m base and a height of 7 m.
3.
A trapezoid has bases of 9 ft and 16 ft and a height of 9 ft.
4.
A parallelogram has a base of 5 m and a height of 7 m.
5.
A triangle has a base of 20 ft and a height of 10 ft.
6.
A trapezoid has bases of 5 cm and 13 cm and a height of 5 cm.
7.
A trapezoid has bases of 10 in and 14 in and a height of 4 in.
8.
A house shape is a rectangle 20 ft wide and 9 ft tall, with a triangle roof on top that has the same 20 ft base and a height of 2 ft.
9.
A house shape is a rectangle 10 m wide and 3 m tall, with a triangle roof on top that has the same 10 m base and a height of 2 m.
10.
A house shape is a rectangle 14 cm wide and 5 cm tall, with a triangle roof on top that has the same 14 cm base and a height of 2 cm.

Answer key: Area of polygons

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 20 cm²
4 × 5 = 20
2. 125 m²
Rectangle: 10 × 9 = 90Triangle: 12 × 10 × 7 = 35Total: 125
3. 112.5 ft²
12 × (9 + 16) × 9= 12 × 25 × 9 = 112.5
4. 35 m²
5 × 7 = 35
5. 100 ft²
12 × 20 × 10 = 100
6. 45 cm²
12 × (5 + 13) × 5= 12 × 18 × 5 = 45
7. 48 in²
12 × (10 + 14) × 4= 12 × 24 × 4 = 48
8. 200 ft²
Rectangle: 20 × 9 = 180Triangle: 12 × 20 × 2 = 20Total: 200
9. 40 m²
Rectangle: 10 × 3 = 30Triangle: 12 × 10 × 2 = 10Total: 40
10. 84 cm²
Rectangle: 14 × 5 = 70Triangle: 12 × 14 × 2 = 14Total: 84

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About area of polygons

Area is the space inside a flat shape, measured in square units. A rectangle is length × width and a parallelogram is base × height. A triangle is half of a parallelogram, so its area is 12 × base × height, and a trapezoid is 12 × (base 1 + base 2) × height. Split odd shapes into these simpler ones.

Worked example 1

A rectangle is 14 cm long and 13 cm wide.

Step 1.14 × 13 = 182

Answer: 182 cm²

Worked example 2

A trapezoid has bases of 4 in and 7 in and a height of 9 in.

Step 1.12 × (4 + 7) × 9
Step 2.= 12 × 11 × 9 = 49.5

Answer: 49.5 in²

Worked example 3

A triangle has a base of 11 m and a height of 3 m.

Step 1.12 × 11 × 3 = 16.5

Answer: 16.5 m²

Watch out for

The height must meet the base at a right angle. A slanted side is not the height.
Don’t forget the 12 for triangles and trapezoids.
Area is in square units, like cm², because you are counting squares.

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