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Surface Area of a Prism

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Surface Area of a Prism

Study Guide

Key Definition

The lateral surface area of a prism is the sum of the areas of its lateral faces. The total surface area is the sum of the areas of its lateral faces and its two bases. The general formula for the lateral surface area of a right prism is $L.S.A. = p \times h$, where $p$ represents the perimeter of the base and $h$ represents the height of the prism.

Important Notes

In a right prism, the lateral edges are perpendicular to the bases.
The total surface area formula is $T.S.A. = p \times h + 2 \times B$, where $B$ is the area of the base.
For triangular prisms, calculate the base area using $\frac{1}{2} \times \text{base} \times \text{height}$.
Always ensure units are consistent when calculating areas.
Oblique prisms require separate calculations for lateral faces and bases.

Mathematical Notation

$\times$ represents multiplication

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

$\sqrt{x}$ represents the square root of $x$

$L.S.A.$ stands for Lateral Surface Area

$T.S.A.$ stands for Total Surface Area

Remember to use proper notation when solving problems

Why It Works

The formulas derive from summing the areas of the geometric shapes forming the prism's surfaces, ensuring a complete surface area measurement.

Remember

Always consider the shape and dimensions of the base when applying surface area formulas.

Quick Reference

Lateral Surface Area:$L.S.A. = p \times h$

Total Surface Area:$T.S.A. = p \times h + 2 \times B$

Understanding Surface Area of a Prism

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Video explanation of this concept

Beginner

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Beginner Explanation

The surface area of a prism is the total area covering the outside of the shape, calculated with $p \times h + 2 \times B$ for a right prism.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the lateral surface area of a prism with a base perimeter of $12 \text{ inches}$ and a height of $8 \text{ inches}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a triangular banner with a base perimeter of $12 \text{ inches}$ and a height of $8 \text{ inches}$. Calculate the lateral surface area.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A prism has a base area of $30 \text{ cm}^2$ and a height of $10 \text{ cm}$. What is the total surface area if the base perimeter is $20 \text{ cm}$?

Challenge Quiz

Single Choice Quiz

Advanced

A prism has a trapezoidal base with a perimeter of $28 \text{ cm}$, a height of $10 \text{ cm}$, and a base area of $40 \text{ cm}^2$. What is the total surface area?

Recap

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Review key concepts and takeaways