8.3 Perimeter and Area 475 Perimeter and Area SECTION 8.3 LEARNING GOALS Upon completion of this section, you will be able to: 7 Understand and use formulas for the perimeter and area of polygons. 7 Solve problems involving the Pythagorean theorem. 7 Understand and use formulas for the circumference and area of circles. 7 Solve problems involving square unit conversions. Perimeter and Area The perimeter , P, of a two-dimensional figure is the sum of the lengths of the sides of the figure. In Figs. 8.25 and 8.26, the sums of the lengths of the red line segments are the perimeters. Perimeters are measured in the same units as the sides. For example, if the sides of a figure are measured in feet, the perimeter will be measured in feet. The area , A, is the measure of the region within the boundaries of the figure. For example, in Fig. 8.25 the area of the pentagon refers to the measure of the blue region within the boundary of the pentagon. Area is measured in square units. For example, if If you were to walk around the outside edge of a pickleball court, how far would you walk? If you had to place floor tiles that each measured 1 foot by 1 foot on a basketball court, how many tiles would you need? In this section, we will study the geometric concepts of perimeter and area that are used to answer these and other questions. Why This Is Important The concepts of area and perimeter are involved in many real-life applications of geometry. These include calculating the cost of flooring for your home, calculating the amount of fencing needed for your yard, and determining the best value when purchasing pizza! Challenge Problem/Group Activity 81. Height of a Wall You wish to measure the height of an inside wall of a warehouse. No ladder tall enough to measure the height is available. You place a mirror on the floor. You then move away from the mirror until you can see the reflection of the top of the wall in it, as shown in the following figure. a) Explain why triangle HFM is similar to triangle TBM. ( Hint : In the reflection of light the angle o f incidence , HMF, equals the angle of reflection , TMB. Thus, = HMF TMB. ) = m HMF m TMB, = m HFM m TBM, = m MHF m MTB b) If your eyes are 5 ft 1 2 above the floor and you are 2 ft 1 2 from the mirror and the mirror is 20 ft from the wall, how high is the wall? 44 ft F H M B T Recreational Mathematics 82. Distance Across a Lake a) In the following figure, = m CED m ABC. Explain why triangles ABC and DEC must be similar. = m CED m ABC, = m ACB m DCE, = m BAC m CDE b) Determine the distance across the lake, DE. ≈ 2141.49 ft A B C D E 356.0 ft 543.0 ft 1404.0 ft Lake Joy Research Activities 83. Theodolite Write a paper on the history and use of the theodolite, a surveying instrument. 84. Photographic Process Write a paper on the use of geometry in the photographic process. Include discussions on the use of similar figures. Bhpix/Shutterstock
RkJQdWJsaXNoZXIy NjM5ODQ=