### Unit 9: Perimeter and Area

Two of the most common applications of Geometry are area and perimeter. Owning a home gives you plenty of opportunities to use these concepts. Thinking of buying a cordless electric lawnmower? The manufacturer will give you an estimate of the mower's battery life using square feet. If your yard is extremely large and your mower's battery life is not long enough, it might take you multiple sessions to get it all mowed. Are you buying new carpeting for your home? It is sold in square feet or square yards. You definitely do not want to buy too much carpeting or too little carpeting. You are not just going to eyeball it and make a guess. You will want to measure everything carefully, and then order a bit more, giving yourself some leeway.

Like area, perimeter is often used in home ownership. If you install fencing around your yard, you are going to calculate the perimeter before you buy the fencing. If you are forced to run wiring around the walls of a room, it is vital that you know how much wiring you will need.

**Completing this unit should take you approximately 18 hours.**

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

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

### 9.1: Perimeter and Area Basics

Take notes as you watch this video to understand the basics of area and perimeter. Watch this presentation carefully two or three times to understand how to determine difference of the area and perimeter.

### 9.2: Area of Triangles

Take notes as you watch this video to understand the basics of finding the area and perimeter of a triangle. Watch this presentation carefully two or three times to understand how to find the area and perimeter of a triangle.

Take notes as you watch the video and read this section to learn about area and perimeter of a triangle. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of a triangle.

Complete this assessment, which tests your knowledge on the area of triangles. You can review the concepts associated with these questions from subunit 9.2.

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

Take notes as you watch the video and read this section to learn about area and perimeter of a rectangle. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of a rectangle.

Complete this assessment, which tests your knowledge on the area of squares and rectangles. You can review the concepts associated with these questions from subunit 9.3.

### 9.4: Area of a Parallelogram

Take notes as you watch the video and read this section to learn about area of a parallelogram. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area of a parallelogram.

### 9.5: Area and Perimeter of Trapezoids

Take notes as you watch the video and read this section to learn about area and perimeter of trapezoids. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of trapezoids.

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

Take notes as you watch the video and read this section to learn about area and perimeter of rhombuses and kites. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of rhombuses and kites.

Complete this assessment, which tests your knowledge on the area of trapezoids, rhombi, and kites. You can review the concepts associated with these questions from subunits 9.5 and 9.6.

### 9.7: Area and Perimeter of Similar Polygons

Take notes as you watch the video and read this section to learn about area and perimeter of similar polygons. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of similar polygons.

### 9.8: Circumference

Take notes as you watch the video and read this section to learn about the circumference of a circle. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for circumference of a circle.

### 9.9: Arc Length

Take notes as you watch the video and read this section to learn about the arc length of a circle. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for arc length of a circle.

### 9.10: Area of a Circle

Take notes as you watch the video and read this section to learn about the area of a circle. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for area of a circle.

Complete this assessment, which tests your knowledge on the area of circles. You can review the concepts associated with these questions from subunit 9.10.

### 9.11: Area of Composite Shapes

Take notes as you watch this video to understand the basics of finding the area of composite shapes. Watch this presentation carefully two or three times to understand how to find the area of composite figures.

Take notes as you watch the video and read this section to learn about the areas of composite figures. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for areas of composite figures.