6.G.1: Area of Triangles and Polygons
Also written as 6.G.A.1 and CCSS.MATH.CONTENT.6.G.A.1 · Cluster: Solve real-world and mathematical problems involving area, surface area, and volume.
The Official Wording
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Common Core State Standards, Grade 6, Geometry · Read it at the source · Checked October 14, 2026
What 6.G.1 Means in Plain English
Sixth graders find the area of triangles, trapezoids and irregular polygons by cutting them into rectangles and triangles, or boxing them in one rectangle and subtracting the corners. A trapezoid with parallel sides 10 and 16, 6 units tall, becomes a 10 × 6 rectangle plus two triangles.
The shapes show up as garden beds, floor plans and kites, so the question is which cuts make the arithmetic easy. In 7th grade the same decomposing solves area, surface-area and volume problems with composite figures (7.G.6), and circles get their own formula (7.G.4).
6.G.1 I Can Statements
- I can find the area of a triangle with ½ × base × height.
- I can cut a polygon into rectangles and triangles and add their areas.
- I can box a shape in a rectangle and subtract the corners.
6.G.1 Worked Example
A trapezoid garden bed, cut into a rectangle and two right triangles, then checked by boxing it in.
A garden bed is a trapezoid. Its two parallel sides are 10 ft and 16 ft, and the distance between them is 6 ft. What is its area?
- Draw the shape and drop a vertical line from each end of the short side. That cuts the trapezoid into a rectangle in the middle and a right triangle at each end.Rectangle 10 ft × 6 ft, plus two right triangles
- The rectangle is 10 across and 6 tall.A = 10 × 6 = 60 ft²
- The long side is 16 and the rectangle uses 10 of it, so 6 ft is left over, 3 ft at each end. Each triangle has base 3 and height 6, and a right triangle is half of a 3 × 6 rectangle.A = ½ × 3 × 6 = 9 ft² each
- Add the pieces.60 + 9 + 9 = 78 ft²
Check it: Compose instead: box the trapezoid in a 16 × 6 rectangle, 96 ft². The two corners you cut off are 9 ft² each, so 96 − 18 = 78 ft². Same area both ways.
Common Mistakes with 6.G.1
Forgetting the half for triangles
Triangle with base 3 and height 6: 3 × 6 = 18 ft²
Try this: Have students draw the rectangle around the triangle first and shade the half that is the triangle, so ½ stays in the formula.
Using a slanted side as the height
Sides 5, 5 and 6, base 6: A = ½ × 6 × 5 = 15
Try this: Ask where the right angle is. Height meets the base at 90°, so here it is 4, not 5, and the area is 12.
Counting the corners twice
Rectangle 16 × 6 = 96 plus triangles 9 + 9 = 114 ft²
Try this: Label every length on the drawing first: the rectangle spans only the 10 ft side, and the 6 extra feet belong to the triangles.
Where 6.G.1 Fits
Practice 6.G.1
Quick Check
- Find the area of a right triangle with legs 8 cm and 5 cm.
- A parallelogram has a base of 12 in and a height of 7 in. What is its area?
- An L-shaped room is 14 ft by 10 ft with a 6 ft by 4 ft corner missing. What is its floor area?