Area Problem Solving - Varsity Tutors

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Area Problem Solving

Study Guide

Key Definition

The area of a shape is the amount of space inside the boundary of the shape. It is measured in square units.

Important Notes

  • The area of a rectangle is given by $A = \text{length} \times \text{width}$
  • The area of a triangle is given by $A = \frac{1}{2} \times \text{base} \times \text{height}$
  • The area of a circle is given by $A = \pi \times \text{radius}^2$
  • To find the area of a complex shape, try breaking it up into simpler shapes whose area you can calculate.

Mathematical Notation

$\times$ means multiplication$\frac{a}{b}$ means a divided by bRemember to use proper notation when solving problems

Why It Works

Area formulas work because they measure the number of square units needed to cover a surface.

Remember

Never forget to include your units of measurement when solving for area.

Quick Reference

Area of Rectangle:$\text{length} \times \text{width}$Area of Triangle:$\frac{1}{2} \times \text{base} \times \text{height}$Area of Circle:$\pi \times \text{radius}^2$

Understanding Area Problem Solving

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

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Beginner Explanation

The area of a shape can be calculated using simple formulas. For example, the area of a rectangle is $\text{length} \times \text{width}$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the area of a rectangle with length 6 units and width 8 units?

A$14 \text{ square units}$B$24 \text{ square units}$C$48 \text{ square units}$D$52 \text{ square units}$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Finding Area of a Shaded Region

A rectangle has a square cut out of its center. The dimensions of the rectangle are 6 units by 8 units, and each side of the square is 2 units. What is the area of the shaded part?Show AnswerClick to reveal the detailed solution for this question exercise.3

Advanced Challenge

Thinking ExerciseAdvanced

Think About This

A complex shape is made up of 3 squares and a rectangle. All the squares have sides of 3 units, and the rectangle has dimensions of 3 units by 12 units. What is the total area of the shape?

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

Recap

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Review key concepts and takeaways

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