Review: Classifying Polygons

Lesson 1-8: Perimeter, Circumference and Area Goal: Find the perimeter or circumference of basic shapes. Find the area of basic shapes.

Perimeter, Circumference, and Area:

Example 1: Finding the Perimeter of a Rectangle The botany club members are designing a rectangular garden for the courtyard of your school. They plan to place edging on the outside of the path. How much edging material will they need? Find the perimeter of the garden including the path. 𝑷=𝟐𝒃+𝟐𝒉 =𝟐 𝟏𝟔+𝟒+𝟒 +𝟐 𝟐𝟐+𝟒+𝟒 =𝟐 𝟐𝟒 +𝟐 𝟑𝟎 =𝟒𝟖+𝟔𝟎 =𝟏𝟎𝟖 WE will need 108 ft of edging material.

Example 2: Finding Circumference What is the circumference of the circle in terms of 𝜋? What is the circumference of the circle to the nearest tenth? ⊙𝑀 𝐶=𝜋𝑑 =𝜋 15 ≈47.1238898 The circumference of ⊙𝑀 is 15𝜋 in, or about 47.1 in. ⨀𝑇 𝐶=2𝜋𝑟 =2𝜋 4 =8𝜋 ≈25.13274123 The circumference of ⊙𝑇 is 8𝜋 cm, or about 25.1 cm.

Example 3: Finding Perimeter in the coordinate Plane What is the perimeter of ∆𝑬𝑭𝑮? 𝐸𝐹= 6−(−2) =8 𝐹𝐺= 3−(−3) =6 𝐸𝐺= (3− −3 ) 2 + (6−(−2)) 2 = 6 2 + 8 2 = 36+64 = 100 =10 𝑃=𝐸𝐹+𝐹𝐺+𝐸𝐺=8+6+10=24 The perimeter of ∆𝐸𝐹𝐺 is 24 units.

Example 4: Finding Area of a Rectangle You want to make a rectangular banner similar to the one at the right. The banner shown is 2 1 2 ft wide and 5 ft high. To the nearest square yard, how much material do you need? Convert dimensions. W: 5 2 𝑓𝑡∙ 1𝑦𝑑 3𝑓𝑡 = 5 6 𝑦𝑑 H: 5𝑓𝑡∙ 1𝑦𝑑 3𝑓𝑡 = 5 3 𝑦𝑑 Find the area. 𝐴=𝑏ℎ = 5 6 ∙ 5 3 = 25 18 The area of the banner is 25 18 , or 1 7 18 square yards ( 𝑦𝑑 2 ). We will need 2 𝑦𝑑 2 of material.

Example 5: Finding Area of a Circle What is the area of ⊙𝐾 in terms of 𝜋? Find the radius. 𝑟= 16 2 , 𝑜𝑟 8 Use the radius to find the area. 𝐴=𝜋 𝑟 2 =𝜋 8 2 =64𝜋 The area of ⊙𝐾 is 64𝜋 𝑚 2

Example 6: Finding Area of an Irregular Shape What is the area of the figure at the right? Separate the figure into known shapes. Find 𝐴 1 , 𝐴 2 , and 𝐴 3 . 𝐴𝑟𝑒𝑎=𝑏ℎ 𝐴 1 =3∙3=9 𝐴 2 =6∙3=18 𝐴 3 =9∙3=27 Find the total area of the figure. 𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎=9+18+27=54 The area of the figure is 54 𝑐𝑚 2

Classwork/Homework: Pp 64 – 66 #’s 8 – 46 even