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Squares: Area and Perimeter

Master squares: area and perimeter with interactive lessons and practice problems! Designed for students like you!

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Squares: Area and Perimeter

Study Guide

Key Definition

A square is a quadrilateral with four equal sides and four right angles. The area of a square with side length $a$ is $A = a^2$, and its perimeter is $P = 4a$.

Important Notes

All sides of a square are equal: $AB = BC = CD = DA$
All angles in a square are right angles: $90^\circ$
A square is a rectangle with equal sides
A square is also a rhombus with right angles
The area of a square is calculated using $a^2$
The perimeter of a square is calculated using $4a$
The diagonal of a square relates to the side by $d = a \sqrt{2}$, so $a = \frac{d}{\sqrt{2}}$

Mathematical Notation

$a$ side length

$P$ perimeter

$A$ area

$d$ diagonal

$\sqrt{2}$ square root of 2

Remember to use proper notation when solving problems

Why It Works

A square has both equal sides (like a rhombus, $AB = BC = CD = DA$) and right angles (like a rectangle, $90^\circ$ each). These combined properties define its unique, regular shape and lead to fixed formulas for its area and perimeter.

Remember

The perimeter of a square is $4a$, and the area is $a^2$.

Quick Reference

Area:$a^2$

Perimeter:$4a$

Understanding Squares: Area and Perimeter

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A square has four equal sides and four right angles.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the perimeter of a square with side length $5$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You are designing a square garden with side length $10$ units on a coordinate plane where one corner is at (0,0) and the opposite corner is at (10,10). Calculate the area to know how much soil you need.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If the area of a square is $64$ square units, what is the length of one side?

Challenge Quiz

Single Choice Quiz

Advanced

A square has a diagonal of length $\sqrt{50}$. What is the length of each side?

Recap

Watch & Learn

Review key concepts and takeaways