# Writing & Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures

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• 0:01 Geometric Figures
• 0:53 Using Algebraic Expressions
• 3:46 Lesson Summary

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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Learning more about algebraic expressions and geometric figures will help you solve problems that occur in your life. In this lesson, you will use the perimeter of a two-dimensional geometric shape to solve a real-world problem.

## Geometric Figures in Real Life

I just bought this awesome new couch. I'm really excited because now I can host football parties at my house and invite all of my friends. The problem is, I don't know which wall in my living room my couch will fit on.

The living room and couch represent our first vocabulary word: 2-dimensional geometric figures. 2-dimensional geometric figures are flat figures that have width and height. These figures can be drawn on a piece of paper; they do not have thickness. In this lesson, I am not evaluating the thickness of the couch or living room.

The perimeter of my living rooms is 50 feet, but I don't know the size of each wall, and I don't know how big the couch is. Perimeter is the distance all the way around an object. In this case, the perimeter of the living room is the length of all of the walls added together.

## Algebraic Expressions for 2D Geometric Figures

The long walls are 5x long, and the short walls are 2x + 4 long.

My couch is x^2 + 2 on the long sides and x width on the short sides.

I can find the lengths of the walls in my living room and the length and width of my couch by solving for x.

Remember, perimeter is the distance all the way around the object.

I know that the perimeter of my living room is 50 feet. I also know that the size of each of the long walls is 5x, and the short walls are 2x + 4. I can use the algebraic expression for each of the walls to find x. An algebraic expression is a math problem with at least one variable and no equal sign.

I am going to take each expression for each wall, add them together and make them equal to 50.

5x + 5x + (2x + 4) + (2x + 4) = 50

I can also use the distributive property to write my equation. The distributive property is multiplying an addition expression by multiplying each addend and then adding the product.

2(5x) + 2(2x + 4) = 50

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