Properties of Rectangles

Learn the defining properties of rectangles including equal opposite sides, right angles, and diagonal relationships.

Intermediate20 minLesson

Definition

A rectangle is a quadrilateral (4-sided polygon) with four right angles (90°).

Key Properties of Rectangles

1. Four Right Angles Every interior angle measures exactly

90°

\angle A = \angle B = \angle C = \angle D = 90°

2. Opposite Sides Are Equal and Parallel The two pairs of opposite sides have equal length:

\overline{AB} = \overline{CD} \quad \text{and} \quad \overline{BC} = \overline{AD}

3. Diagonals Are Congruent The two diagonals have the same length:

\overline{AC} = \overline{BD}

4. Diagonals Bisect Each Other Each diagonal cuts the other exactly in half at their intersection point.

Try it now

How many right angles does a rectangle have?

Worked Examples

A rectangle has a length of $12$ cm and a width of $7$ cm. Find its perimeter.

Recall the perimeter formula

Perimeter $= 2 \times (\text{length} + \text{width})$ → $P = 2(l + w)$

Substitute the values

$P = 2 \times (12 + 7)$ → $P = 2 \times 19$

Calculate

$P = 38$ → $38$ cm

Answer: The perimeter is $38$ cm.

Common Mistakes

Confusing rectangles with squares

Why it's wrong: A square IS a special type of rectangle (all angles are 90°), but not all rectangles are squares.

Correct: A rectangle has opposite sides equal. A square has ALL four sides equal. Every square is a rectangle, but not every rectangle is a square.

Forgetting that both diagonals are equal

Why it's wrong: In some quadrilaterals (like parallelograms), diagonals are NOT equal.

Correct: In a rectangle, both diagonals are always congruent (same length). This is a special property!

Using $P = l \times w$ instead of $P = 2(l + w)$

Why it's wrong: Students confuse perimeter (distance around) with area (space inside).

Correct: Perimeter = sum of all sides = $2l + 2w = 2(l + w)$ . Area = $l \times w$ .

Interactive Visual

Area and perimeter

Length l8Width w5

Area40

$A = l \cdot w = 8 \cdot 5 = 40$

Perimeter26

$P = 2(l + w) = 2(8 + 5) = 26$

Diagonal9.43

$d = \sqrt{l^2 + w^2} = \sqrt{89} \approx 9.43$

The two diagonals of a rectangle are always equal.

Interactive Sandbox

Expression Calculator

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Practice Problems

15 problems

Problem 1 of 15

Easy

How many right angles does a rectangle have?

Why It Matters

Rectangles are one of the most common shapes in the world around us:

Architecture: Doors, windows, rooms, and buildings are typically rectangular
Technology: Screens, phones, tablets, and monitors are all rectangles
Sports: Soccer fields, basketball courts, and swimming pools use rectangular shapes
Design: Books, papers, cards, and photographs are rectangular

Understanding rectangle properties helps with construction, design, and solving real-world measurement problems!

Real World Applications

Home Improvement: Flooring

Calculating how much flooring material you need for a rectangular room.

Example:

A room is $5$ m by $4$ m. You need $5 \times 4 = 20$ m² of flooring.

1Try It Yourself

You want to put a fence around a rectangular backyard that is $20$ meters long and $15$ meters wide.

How many meters of fencing do you need?

Step 1: Write the mathematical expression

Use the perimeter formula:

Screen Technology

TV and monitor screens are measured diagonally, but the actual viewing area uses rectangle properties.

Example:

A screen that is $48$ cm wide and $27$ cm tall has an area of $48 \times 27 = 1296$ cm².

2Try It Yourself

A tablet screen is $24$ cm long and $18$ cm wide.

What is the diagonal measurement of the screen?