Area and Perimeter • Topic 2 of 6

Squares

A square is a rectangle with all sides equal, so its area is side² and its perimeter is 4 × side. Because everything depends on one length, a single side determines both, and either measure can be reversed: the side is the square root of the area, or one-fourth of the perimeter. For a square of side 6, the area is 36 and the perimeter is 24. As with rectangles, keep area (square units, the space inside) separate from perimeter (a length around the edge). The SAT often gives the area and asks for the side or perimeter, so be ready to take a square root.

A square of side 6Square66Area = 6² = 36    Perimeter = 4 × 6 = 24

✅ Solved examples

1. A square has side 6. Find its area.
6² = 36.
2. A square has side 6. Find its perimeter.
4 × 6 = 24.
3. A square has area 49. Find its side.
√49 = 7.
4. A square has perimeter 32. Find its side.
32 ÷ 4 = 8.

✏️ Practice — try these, take hints as needed

1. A square has side 9. Find its area.
side².
9².
—
81.
2. A square has side 5. Find its perimeter.
4 × side.
4 × 5.
—
20.
3. A square has area 100. Find its side.
√100.
—
—
10.
4. A square has perimeter 36. Find its side.
36 ÷ 4.
—
—
9.
5. A square has side 12. Find its area.
12².
—
—
144.

📝 Topic test — 8 questions

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