### Unit 9: Perimeter and Area

Calculating area and perimeter are probably the two most common applications of geometry.

For example, if you want to install some carpet you need to measure the size of your space so you know how much carpet you need to buy to cover it (in terms of square feet or square meters). To install a fence, you need to calculate the perimeter of your yard so you know how much lumber you need to buy. To wire a room you need to calculate the perimeter of your room's interior walls so you know how much cable you need to buy and how much your labor and installation will cost (your electrician will likely charge you by the foot).

**Completing this unit should take you approximately 5 hours.**

Upon successful completion of this unit, you will be able to:

- calculate the area and perimeter of triangles and quadrilaterals;
- calculate the area and circumference of a circle;
- calculate the arc length of a circle;
- calculate the area of composite shapes;
- calculate the ratios of areas and perimeters for similar polygons; and
- calculate the scale factor for similar polygons.

- calculate the area and perimeter of triangles and quadrilaterals;

### 9.1: Perimeter and Area Basics

Your first step in this unit is to understand the basic idea of perimeter, area, and the language mathematicians commonly use in these types of problems.

Watch this video to learn how mathematicians talk about these concepts.

### 9.2: Area of Triangles

Let's look at how to calculate the area and perimeter of the different types of geometric shapes we have studied in this course. It may be helpful to keep a list of the different area formulas you encounter in this unit. First, we'll look at triangles.

Read this article and watch the videos. Pay attention to the formula for the area of a triangle, including the special case of right triangles. Note that we use the Pythagorean theorem to calculate the perimeter of a triangle.

Then, complete review questions 1–5 and check your answers.

### 9.3: Area and Perimeter of Rectangles and Squares

Now, let's look at the area and perimeter formulas of rectangles and squares.

Read this article and watch the three embedded videos, which discuss the formulas we use to calculate the area and perimeter of rectangles and squares.

After you have reviewed the material, complete review questions 1–6 and check your answers.

### 9.4: Area of a Parallelogram

The next shape we study is the parallelogram. When you calculate the area of a parallelogram, envision rearranging it into a rectangle, and use the formulas you have just learned.

Read this article and watch the videos. Pay attention to how to "rearrange" a parallelogram into rectangles before calculating its area.

Then, complete review questions 1, 2, 6, 7, 13, and 14 and check your answers.

### 9.5: Area and Perimeter of Trapezoids

Now, let's look at trapezoids.

Read this article and watch the two embedded videos, which highlight the formulas we use to calculate the area and perimeter of a trapezoid.

After you have reviewed the material, complete review questions 1–5 and check your answers.

### 9.6: Area and Perimeter of Rhombuses and Kites

Next, we focus on rhombuses and kites.

Read this article and watch the video which highlight the formulas we use to calculate the area and perimeter of rhombuses and kites.

Then, complete review questions 2, 3, 4, 12, 13, 14, and 15 and check your answers.

### 9.7: Area and Perimeter of Similar Polygons

Here, we explore how to determine the area and perimeter of similar polygons. Similar polygons have identical angles and proportional side lengths.

Read this article and watch the video. These highlight the formulas we use to calculate the area and perimeter of similar polygons. Perimeters and areas of similar polygons are proportional.

### 9.8: Circumference

When studying circles, we use the term circumference to describe the distance around the circle.

Read this article, which explains the circumference formula and gives examples for calculating circumference.

Then, complete the practice questions and check your answers.

### 9.9: Arc Length

The arc length is the length of circumference in a "slice" of a circle defined by an arc.

Read this article and watch the videos. Note the arc length formula. Pay attention to the examples on measuring arc length, finding the radius, and measuring the central angle.

Then, complete review questions 1, 5, and 8 and check your answers.

### 9.10: Area of a Circle

We can now determine the area of a circle. The area of a circle is pi times the radius squared (A = π r²).

Pi is a number – approximately 3.142. It is the circumference of any circle divided by its diameter. The number pi, denoted by the Greek letter π (pronounced "pie"), is one of the most common constants in all of mathematics.Watch this video, which introduces the formula for the area of a circle and an example of using this formula.

Then, take this assessment and check your answers.

### 9.11: Area of Composite Shapes

Lastly, we learn about composite shapes, which are non-standard polygons.

Watch this video to see how we can use what we learned about standard polygons to develop methods for determining the area and perimeter of a composite shape.