• 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.

    • 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.

    • 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.

      • Area and Perimeter of a Triangle URL

        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.

      • Area and Perimeter of a Rectangle URL

        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.

      • Area of a Parallelogram URL

        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.

      • Area and Perimeter of Trapezoids URL

        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.

      • Area and Perimeter of Rhombuses and Kites URL

        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.

      • Area and Perimeter of Similar Polygons URL

        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.

      • Circumference Review URL

        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.

      • Arc Length URL

        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.

    • 9.11: Area of Composite Shapes

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