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Prism

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Prism

Study Guide

Key Definition

A prism is a three-dimensional figure with two congruent polygonal bases and parallelogram faces in between. The volume of a prism is calculated as $V = B \times h$, where $B$ is the area of the base and $h$ is the height.

Important Notes

A prism is named after the shape of its base.
In a right prism, lateral edges are perpendicular to the base.
The surface area of a prism includes all the lateral faces and the two bases.
Prisms are used in real-world applications like architecture and design.
Understanding prisms is crucial for higher-level STEM fields.

Mathematical Notation

$\times$ represents multiplication

$V$ is the volume

$B$ represents the area of the base

$h$ represents height

$P$ is the perimeter of the base

$\cong$ means congruent

Remember to use proper notation when solving problems

Why It Works

Prisms allow us to calculate volumes and surface areas of complex structures using simple formulas like $V = B \times h$.

Remember

A prism's volume is determined by the area of its base and its height. Use $V = B \times h$.

Quick Reference

Volume Formula:$V = B \times h$

Surface Area:$SA = 2B + Ph$, where $P$ is the perimeter of the base

Understanding Prism

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A prism is a shape with two identical bases. Calculate its volume using $V = B \times h$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the volume of a prism with a base area of $20 \text{ cm}^2$ and height of $10 \text{ cm}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Explain the steps you would take to calculate the total surface area of a rectangular prism.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a prism's base is a hexagon, how does the number of sides affect the total surface area?

Challenge Quiz

Single Choice Quiz

Advanced

Calculate the surface area of a prism with base perimeter $15 \text{ cm}$, height $8 \text{ cm}$, and base area $18 \text{ cm}^2$.

Recap

Watch & Learn

Review key concepts and takeaways