Area
In short: Area counts how much flat surface a shape covers in square units, so a 7 by 4 rectangle takes up 28 of them.
6th GradeGeometry6.G.A.1
What is Area?
Imagine tiling a patio with one-foot paving stones and counting them: that count is the area. It answers how much floor, paper or paint a flat region needs, with no gaps and no overlaps.
Units are square inches, square meters and the like. For sides \(\ell\) and \(w\) of a rectangle, \(A = \ell w\). A figure assembled from pieces that do not overlap has the total of its pieces.
How to spot it
- A question asks how much carpet, paint, grass seed or wrapping paper a flat region needs.
- Answers must be written with square units such as ft² or square feet.
- A shape is drawn on a grid and you can count full and partial squares.
- An L-shaped or irregular figure can be cut into rectangles and triangles.
The method
- Identify the shape and write down the lengths that matter, in the same unit.
- Apply the matching formula, such as \(\ell w\) for a rectangle.
- For an L-shape or other combined figure, split it into simple pieces, measure each one and add.
- Label the answer with square units.
Area: solved example
Problem
A community garden in Austin is a rectangle 18 feet long and 11 feet wide, with a 4 foot by 3 foot rectangular shed pad cut out of one corner. How many square feet are left for planting?
Solution
Whole rectangle: \(18 \times 11 = 198\) square feet. Shed pad: \(4 \times 3 = 12\) square feet.
Subtract: \(198 – 12 = 186\). The ground left for planting is 186 square feet.
Try it
Question 1
A poster measures 2.5 feet by 1.5 feet. Find its area.
Show the answer
\(2.5 \times 1.5 = 3.75\) square feet.
Question 2
Why must the answer to a covering problem be written in square units and not just units?
Show the answer
The count is of unit squares that tile the surface, so the unit is multiplied by itself, as in feet times feet.
Area vs. Volume
The first covers a flat surface and is counted in square units. Volume fills a solid and is counted in cubic units. A shoebox lid has the first kind of measure, while the whole box has a volume.
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Whole dictionary: A–Z · 6th Grade · Geometry