Surface Area Of A Pyramid - Varsity Tutors

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Surface Area of a Pyramid

Study Guide

Key Definition

The lateral surface area of a regular pyramid is $L.S.A. = \frac{1}{2}pl$, where $p$ is the perimeter of the base and $l$ is the slant height.

Important Notes

  • The total surface area includes the base: $T.S.A. = \frac{1}{2}pl + B$
  • Perimeter $p$ of a triangular base is the sum of its sides.
  • Perimeter $p$ of a square base is $4s$, where $s$ is the side length.
  • The area of a square base is $s^2$.
  • Non-regular pyramids do not have a defined slant height.

Mathematical Notation

$\times$ represents multiplication$\div$ represents division$\frac{1}{2}$ means half of a quantity$p$ represents perimeter of the base$l$ represents slant heightRemember to use proper notation when solving problems

Why It Works

The formula $L.S.A. = \frac{1}{2}pl$ works because it calculates the sum of the triangular lateral faces.

Remember

Always find the perimeter first to use in $L.S.A. = \frac{1}{2}pl$ and $T.S.A. = \frac{1}{2}pl + B$.

Quick Reference

Lateral Surface Area:$\frac{1}{2}pl$Total Surface Area:$\frac{1}{2}pl + B$

Understanding Surface Area of a Pyramid

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Beginner Explanation

The lateral surface area (L.S.A.) of a pyramid is calculated as $\frac{1}{2} p l$, where p is the base perimeter and l is the slant height. First find p, then multiply by l, and take half of that.Now showing Beginner level explanation.

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

What is the lateral surface area of a pyramid with an equilateral triangular base with side length 8 inches and a slant height of 5 inches? (No diagram is needed.)

A$60 in^2$B$64 in^2$C$72 in^2$D$80 in^2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Imagine building a pyramid-shaped tent with a square base with side length 16 inches and slant height of 17 inches. Calculate the total surface area of the tent.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Given a pyramid with a non-regular base, determine what additional information is needed to calculate the surface area.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Find the total surface area of a pyramid with a hexagonal base of perimeter 48 inches and slant height of 9 inches. The base area is 144 square inches. (No net diagram is needed.)

A$360 in^2$B$384 in^2$C$416 in^2$D$432 in^2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

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