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Similar Polygons: Definition, Examples, and Applications

Grade 12 Math: Master Advanced Concepts & Skills

Geometric constructions

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Classifying triangles

Isosceles and equilateral triangles

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Parallel and perpendicular lines

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Circle geometry

Angles in a circle

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Transformations of 2D shapes

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Non-Euclidean geometries

Combining transformations of functions

Surface area of 3-dimensional shapes

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

We&apos;ve got you covered with our complete help for Grade 12 math, whether it&apos;s Ontario curriculum, <a href="https://www.alberta.ca/writing-diploma-exams.aspx">Diploma exam</a> (Alberta), <a href="http://www.edu.gov.mb.ca/k12/assess/tests/index.html">Provincial test</a> (Manitoba) or <a href="https://www.saskatchewan.ca/residents/education-and-learning/departmental-exams">Departmental exam</a> (Saskatchewan).

Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Geometry 12

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade12math.png

Intro

- Hi. Welcome to this question right here. So we're here to find the perimeter, which is all the sides added up together, of the smaller quadrilateral right here. Okay? So it seems like we&apos;ve got a big one and a small one. Now, I guess it's by assuming they are similar to each other, or else we cannot do this question. So we know the big quadrilateral on the outside is 25.2, 21, 44.1, 33.6. We're looking for this number, this number and that number right there in order to calculate the total perimeter, right? So far we're given. . .the information we have is the 25.2 and the 16.8 here. They are the similar sides of the two figures, right? So figuring out the ratio is the first thing you have to do. So the ratio is take the bigger one, 25.2, divided by the smaller one, 16.8, and let's see what we&apos;ve got. 25.2 divided by 16.8, we have a 1.5, which is a good number. I like that. Okay? So the ratio is one and a half. So it means the bigger one is one and a half times bigger than the smaller one. So how do we figure out the rest of the information? We're just going to do it one at a time. So what happens is this is the big one, right? That is the smaller one. So you can actually just say that 33.6 divided by the smaller one is equal to 1.5. Okay? 
For this missing side right there. So all we have to do is just crisscross these two guys. So mathematically to figure out the answer is actually just 33.6 divided by 1.5. So let me work that out for you right here. So 33.6 divided by 1.5 will give you this missing box, which is 33.5 divided by 1.5. We have 22.33. Okay? 22.33 repeating. So what happens is we're going to go ahead and do the same thing to every single side. Okay? So for the next one right there, we're going to follow the same math. 44.1 divided by 1.5. Okay. Sorry about my writing right there. Let's put 1.5 one more time. So 44.1 divided by 1.5, we&apos;ve got ourselves 29.4. So this is my 29.4 right there. Okay? So I'm going to write down 29.4 on this side. And finally you come down to the last one, the last person right there. It's the 21 divided by 1.5 again. So we&apos;ve got 21 divided by 1.5. It's just 14. How nice. We&apos;ve got a nice number finally. So this one here turns out to be a 14. So to get the total perimeter, guess what? It's just the 16.8, plus the 22.33, plus the 29.4 and finally the 14 at the very last. Okay? 
So 16.8 plus the 22.333 plus the 29.4 and the 14 at the very end. We&apos;ve got ourselves 82.53. Okay? 82.53. And that is your final answer. If you add up all of the sides of the smaller quadrilateral, that is the perimeter. Thanks for watching.

In this lesson, we will learn how to determine whether a pair of polygons is similar to each other. Once we know that the polygons are similar, we can calculate unknowns such as, side lengths, scale factors, and surface areas.

Understanding similar polygons