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1-5 Using Formulas in Geometry The student will be able to : Apply formulas for the perimeter, area and circumference of a circle. What is perimeter? Answer: is the sum of all the sides lengths of a figure. What is area? Area is the space inside a two-dimensional figure. What are some of the difference you see between area and perimeter? Just remember!!! Perimeter is expressed in linear units, such as inches (in.) or meters (m). Area is expressed in square units, such as square centimeters (cm2). Find the area and perimeter of each figure: = 2(6) + 2(4) = 12 + 8 = 20 in. = (6)(4) = 24 in2 Find the area and perimeter of each figure: 24 13 15 Solution: 𝐴𝑟𝑒𝑎 = 𝐴𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒∗ℎ𝑒𝑖𝑔ℎ𝑡 2 15∗13 = 97.5 2 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑎 + 𝑏 + 𝑐 = 15 + 13 + 24 = 52 Lets do the worksheet on area The area of a rectangular fence is 256 𝑓𝑡 2 . If the height of the fence is 11feet . What is the base of the fence. Solution: 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑓𝑒𝑛𝑐𝑒 = 𝑏𝑎𝑠𝑒 ∗ ℎ𝑒𝑖𝑔ℎ𝑡 256 = 11 ∗ 𝑥 then solve for x 256 11 𝑥 = 11𝑥 11 = 23.3 𝑓𝑒𝑒𝑡 The sides of a triangle are (x+5), (3x+5), and (2x4).Find x when the perimeter of the triangle is 60. Solution: 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = adding all the sides of the triangle 60 = 𝑥 + 5 + 3𝑥 + 5 + 2𝑥 − 4 60 = 𝑥 + 3𝑥 + 2𝑥 + 5 + 5 − 4 60 = 6𝑥 + 6 −6 = −6 54 = 6𝑥 54 6 = 6𝑥 6 9=𝑥 = Write and solve the following: The length of a rectangle is 5 inches less than three times its width. The perimeter is 86 inches. Find the length and width. As shown in the following diagram, a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter? What is the diameter of a circle? Answer: is a segment that passes through the center of the circle and whose endpoints are on the circle. What is the radius of the circle? Answer: is a segment whose endpoints are the center of the circle and a point on a circle. What is the circumference? Answer: Is the distance around the circle. The ratio of a circle’s circumference to its diameter is the same for all circles. This ratio is represented by the Greek letter (pi). The value of is irrational. Pi is often approximated as 3.14 or 22/7 . What is the area of the circle ? Answer: is the space inside the circle. Find the circumference and area of a circle with radius 8 cm. Use the key on your calculator. Then round the answer to the nearest tenth. 50.3 cm 201.1 cm2 Find the circumference and area of a circle with diameter 14m. Lets do the worksheet on area and circumference. Lets do problems 20-26 and 28. From page 39 Today we learned about the areas of difference shapes as well as the circumference of the circle. Tomorrow we are going to continue with 1.6