CCSS.Math.Content.6.G.A.1
The Standard
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 for Mathematics · Geometry
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the area of triangles, quadrilaterals, and irregular polygons. They split shapes into rectangles and triangles, calculate each part, and combine the areas to solve problems.
What Mastery Looks Like
- A student can choose useful lines to split a polygon into familiar shapes. The student calculates each area accurately, combines the results, and labels the answer with square units.
Common Misconceptions
- Students may forget to divide by two when finding a triangle's area. They may use a slanted side instead of the perpendicular height. When splitting polygons, they may leave gaps, overlap pieces, or omit square units.
How to Assess It
- Exit ticket: A trapezoid has parallel bases of 8 cm and 12 cm and a height of 5 cm. Decompose it, label each piece, and show an area equation.
Lesson moves
Ways to Teach It
Give pairs grid-paper polygons to cut apart and rearrange into rectangles, then record each piece's area and the total.
Ask, “How can two different decompositions produce the same area?” Students sketch and explain both methods.
Play Area Match: students pair shape cards with decomposition diagrams and area equations, then check matches with a partner.
Use a classroom floor plan with labeled dimensions and have students calculate the area needing carpet, excluding a triangular storage space.
Free download
Printable 6.G.A.1 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.6.G.A.1, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetBefore This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.4.MD.A.3
Students use rectangle area as the base for composing polygons and for seeing triangle area as half a rectangle.
- CCSS.Math.Content.5.NF.B.4b
Rectangle area with fractional side lengths supports finding component areas when polygons are decomposed into rectangles and triangles.
- CCSS.Math.Content.4.G.A.2
Recognizing right triangles and perpendicular sides supports decomposing polygons into usable triangles and rectangles for area.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.G.B.6
Composing and decomposing shapes by area supports understanding area-based explanations of why the side-square areas in Pythagorean proofs match.
- CCSS.Math.Content.6.G.A.4
Surface area from nets requires finding and adding areas of rectangular and triangular faces, the same decomposition area work from 2D figures.
- CCSS.Math.Content.7.G.B.4
Decomposing shapes and using area formulas supports understanding the circle area derivation, though circumference adds new ideas.
- CCSS.Math.Content.7.G.A.1
Finding areas of triangles and polygons supports computing actual areas from scale drawings when figures are not simple rectangles.
- CCSS.Math.Content.7.G.B.6
Area decomposition of triangles and polygons carries into composite area and finding surface area from the faces of prisms.
Keep exploring
Related Standards
- CCSS.Math.Content.3.MD.D.8
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side len...
- CCSS.Math.Content.1.G.A.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectang...
- CCSS.Math.Content.HSG-SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
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