Master

Trapezoids: Area and Perimeter

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

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Trapezoids: Area and Perimeter

Study Guide

Key Definition

A trapezoid is a four-sided shape with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs.

Important Notes

The area of a trapezoid can be calculated using $\frac{b_1 + b_2}{2} \times h$
The perimeter of a trapezoid is the sum of all four sides: $b_1 + b_2 + l_1 + l_2$
An isosceles trapezoid has equal angles at each base
Height (h) is the perpendicular distance between the bases
Trapezoids can be found in various real-world structures

Mathematical Notation

$\frac{a}{b}$ represents a fraction

$+$ represents addition

$\times$ represents multiplication

$b_1$ and $b_2$ are the lengths of the bases

$h$ is the height

$l_1$ is the length of the first leg

$l_2$ is the length of the second leg

Remember to use proper notation when solving problems

Why It Works

The formula for the area of a trapezoid is derived from breaking the shape into simpler components, such as triangles and rectangles, and applying known formulas.

Remember

For a trapezoid: Area = $\frac{b_1 + b_2}{2} \times h$; Perimeter = $b_1 + b_2 + l_1 + l_2$

Quick Reference

Area Formula:$\frac{b_1 + b_2}{2} \times h$

Perimeter Formula:$b_1 + b_2 + l_1 + l_2$

Understanding Trapezoids: Area and Perimeter

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A trapezoid has two parallel sides, and its area is calculated using $\frac{b_1 + b_2}{2} \times h$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the area of a trapezoid with bases $b_1 = 3 \text{ cm}$ and $b_2 = 4 \text{ cm}$, and height $h = 5 \text{ cm}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a trapezoidal garden with bases of $6 \text{ m}$ and $10 \text{ m}$, and a height of $4 \text{ m}$. What is the area?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can you find the perimeter of a trapezoid with sides $3 \text{ cm}, 4 \text{ cm}, 5 \text{ cm},$ and $6 \text{ cm}$?

Challenge Quiz

Single Choice Quiz

Advanced

If a trapezoid has bases $b_1 = x$ and $b_2 = 2x$, and a height $h = \sqrt{3}x$, what is the area in terms of $x$?

Recap

Watch & Learn

Review key concepts and takeaways