Key takeaway: Area is the amount of flat surface a shape covers, measured by counting unit squares, so a rectangle 14 feet by 9 feet covers 126 square feet.
Grade 66.G.A.1Geometry and Measurement
Definition of Area
The area of a flat shape tells how much surface lies inside its boundary. To measure it, imagine tiling the shape with squares of the same size and counting them. If every tile is one foot on each side, the answer comes out in square feet.
For a rectangle, rows of tiles make multiplication a shortcut: the number of tiles in a row times the number of rows. Irregular shapes are split into rectangles, triangles or other known pieces, and the pieces are added. Shapes with a missing corner can be treated as a big rectangle with a smaller one removed. The result is always reported in square units, never in plain units of length.
Formula and notation
For a rectangle with length \(\ell\) and width \(w\):
\[A = \ell \times w\]
Units are squared: feet become \(\text{ft}^2\), meters become \(\text{m}^2\), and inches become \(\text{in}^2\). A composite shape uses \(A = A_1 + A_2\) for joined pieces, or \(A = A_{\text{big}} – A_{\text{cut}}\) for a removed piece.
Key facts
- Area counts the square units inside a boundary; it ignores the length of the boundary itself.
- Doubling every side length of a shape multiplies its area by four.
- Two shapes with very different looks can cover the same amount of floor.
- Convert all lengths to the same unit before multiplying.
Area example
A gym floor is shaped like a 14-yard by 9-yard rectangle with a 5-yard by 4-yard corner cut out for a stage. Find the area of floor that needs varnish.
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The full rectangle covers \(14 \times 9 = 126\) square yards.
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The missing corner covers \(5 \times 4 = 20\) square yards.
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Subtract: \(126 – 20 = 106\).
The floor measures 106 square yards.
Common mistake
Watch out
Dina claims a 12-foot by 7-foot garden covers \(2(12 + 7) = 38\) feet.
Why it is wrong
That formula gives the perimeter, the distance around the garden, measured in feet. The surface inside is \(12 \times 7 = 84\) and must be written in square feet, \(84\text{ ft}^2\). Mixing the two up is one of the most common slips in geometry.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Geometry and Measurement