How Do You Use Similar Figures to Find the Area of a Polygon?

Note:

When you're working with similar figures, knowing the scale factor can help you find all sorts of pieces including side measurements and area. This tutorial shows you how to use the scale factor to help find the area of one of the figures.

Keywords:

problem
similar figures
polygon
area
proportional
squared
area length

Background Tutorials

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
- What's a Ratio?
  
  Ratios are everywhere! The scale on a map or blueprint is a ratio. Ingredients sometimes need to be mixed using ratios such as the ratio of water to cement mix when making cement. Watch this tutorial to learn about ratios. Then think of some ratios you've encountered before!
Write and evaluate numerical expressions involving whole-number exponents.
- How Do You Square a Number?
  
  Want to square a number? Just take the number and multiply it by itself! If you square an integer, you get a perfect square! Check out squaring in this tutorial!
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- What's a Proportion?
  
  The idea of proportions is that a ratio can be written in many ways and still be equal to the same value. That's why proportions are actually equations with equal ratios. This is a bit of a tricky definition, so make sure to watch the tutorial!
Use proportional relationships to solve multistep ratio and percent problems.
- How Do You Solve a Word Problem Using a Proportion?
  
  This tutorial provides a great real world application of math. You'll see how to use the scale from a blueprint of a house to help find the actual height of the house. This tutorial shows you how to use a proportion to solve!
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
- How Do You Find the Area of a Rectangle?
  
  To find the area of a rectangle, multiply the length times the width! This tutorial will show you how to find the area of a rectangle. Check it out!
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
- What are Similar Figures?
  
  Looking at two figures that are the same shape and have the same angle measurements? You have similar figures! Learn all about it in this tutorial!
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
- How Do You Solve an Equation Using Division?
  
  Solving an equation for a variable? Perform the order of operations in reverse! Check it out in this tutorial.
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- How Do You Find a Scale Factor in Similar Figures?
  
  Have similar figures? Want to find the scale factor? Then check out this tutorial! You'll see how to use measurements from similar figures to create a ratio and find the scale factor.
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
- What is a Triangle?
  
  You can't learn everything about math without dealing with triangles. Did you know that there are different types of triangles? Check out this tutorial, and learn about triangles and their different types!

How Do You Use Similar Figures to Find the Area of a Polygon?

How Do You Use Similar Figures to Find the Area of a Polygon?

Note:

Keywords:

Background Tutorials

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Write and evaluate numerical expressions involving whole-number exponents.

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Use proportional relationships to solve multistep ratio and percent problems.

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.