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Rectangles

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Rectangles

Study Guide

Key Definition

A rectangle is a parallelogram with four right angles. The perimeter is calculated as $P = 2l + 2w$ and the area as $A = l \times w$.

Important Notes

All rectangles have four right angles.
The opposite sides of a rectangle are equal.
A rectangle is a type of parallelogram.
The diagonal of a rectangle can be found using the Pythagorean theorem: $d = \sqrt{l^2 + w^2}$
In a rectangle, $l$ represents length and $w$ represents width.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Rectangles have equal opposite sides and four right angles, allowing us to use straightforward formulas for calculating perimeter and area: $P = 2l + 2w$ and $A = l \times w$.

Remember

Always check for right angles in rectangles and use $P = 2l + 2w$ and $A = l \times w$ for calculations.

Quick Reference

Perimeter:$P = 2l + 2w$

Area:$A = l \times w$

Understanding Rectangles

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A rectangle is a four-sided figure with opposite sides equal and four right angles; its perimeter is given by P = 2l + 2w and its area by A = l × w.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the area of a rectangle with $l = 5$ and $w = 3$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a rectangular garden with a length of $8$ meters and a width of $4$ meters.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine if a shape with sides $6$ and $8$ and diagonal $10$ is a rectangle.

Challenge Quiz

Single Choice Quiz

Advanced

If the perimeter of a rectangle is $20$ and the length is $7$, what is the width?

Recap

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Review key concepts and takeaways