Quadrilaterals • Topic 2 of 5

Rectangles

A rectangle is a parallelogram with four right angles. It keeps all parallelogram properties — opposite sides equal and parallel — and adds that every angle is 90° and the two diagonals are equal in length. Its perimeter is 2(length + width) and its area is length × width. Because the diagonals are equal and the angles are right, the Pythagorean theorem gives the diagonal as √(length² + width²). The SAT uses rectangles for perimeter, area and diagonal questions, and as frames for composite figures. Keep perimeter (a sum around the edge) distinct from area (the space inside) — mixing them up is the classic error.

A rectangle with right angles, sides labeled, and equal diagonals drawnRectanglel = 8w = 5Four right angles; diagonals are equal in length

✅ Solved examples

1. A rectangle is 8 long and 5 wide. Find its perimeter.
2(8 + 5) = 26.
2. The same rectangle — find its area.
8 × 5 = 40.
3. A rectangle has length 12 and width 9. Find the diagonal.
√(144 + 81) = √225 = 15.
4. How many right angles does a rectangle have?
Four.

✏️ Practice — try these, take hints as needed

1. A rectangle is 10 long and 4 wide. Find its perimeter.
2(l + w).
2(10 + 4).
—
28.
2. A rectangle is 7 by 6. Find its area.
Length × width.
7 × 6.
—
42.
3. A rectangle has length 8 and width 6. Find the diagonal.
√(8² + 6²).
√100.
—
10.
4. A rectangle is 15 long and 5 wide. Find its perimeter.
2(15 + 5).
—
—
40.
5. In a rectangle, the two diagonals are:
Compare their lengths.
—
—
Equal.

📝 Topic test — 8 questions

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