Transcript Bellwork
Bellwork • Find the area of the shapes described: Answers: 1. Rectangle with sides 4 inches by 7 inches. 1. 28 inches2 2. Square with side 8 yards. 2. 64 yards2 3. Rectangle with sides 2 meters by 11 meters. 3. 22 meters2 4. Square with side 6 feet. 4. 36 feet2 5. Rectangle with sides 2 feet by 6 inches. 5. 144 inches2 or 1 foot2 Pre-College Math AREA: RECTANGLES, SQUARES, PARALLELOGRAMS AND TRIANGLES Area • Area is defined as the extent or measurement of a surface. • This means that it is given by two dimensions (usually length and width) • This requires then that the result be given a two dimensional notation, thus we add the superscript 2 to the units used. This denotes the units of measure (feet, inches, meters, etc) and tells the person looking at the information that it is in two dimensional space (thus the reason for the 2). The Area of a Rectangle • Many of you already know how to find the area of a rectangle • This formula is generalized by 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ. However, these two can be substituted with any two directions of a rectangular parcel, such as height or depth. Area of a Square • The area of the square is much the same as that of a rectangle (since all squares are rectangles). However, since all the sides of the square are the same we can simplify the 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ equation to becoming 𝑠𝑖𝑑𝑒 × 𝑠𝑖𝑑𝑒 or 𝑠𝑖𝑑𝑒 2 . Area of a Parallelogram • The area of a parallelogram is given by 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡. • Thus for the given picture, the area would be given by 𝐴𝑟𝑒𝑎 = 𝑏 × ℎ. Why does that work?? By making one cut from a vertex of the parallelogram perpendicularly to the opposite side, we create a triangle which can be placed on the opposite side of the parallelogram, thus turning it into a rectangle with dimensions 𝑏 × ℎ. So what about the area of a triangle?? • The area of a triangle with base, 𝑏, and height, ℎ, can be demonstrated as being one half the area of a parallelogram with the same base and height. 1 • Thus the area of a triangle is: 𝐴𝑟𝑒𝑎 = (𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡) 2 Example 1: Find the area 1 𝐴𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 2 1 𝐴𝑟𝑒𝑎 = 6.3 𝑖𝑛𝑐ℎ𝑒𝑠 × 8 𝑖𝑛𝑐ℎ𝑒𝑠 2 1 𝐴𝑟𝑒𝑎 = 50.4 𝑖𝑛𝑐ℎ𝑒𝑠 2 2 𝐴𝑟𝑒𝑎 = 25.2 𝑖𝑛𝑐ℎ𝑒𝑠 2 Example 2: Find the missing information 1 𝐴𝑟𝑒𝑎 = 36.4 𝑓𝑒𝑒𝑡 2 2 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 1 = 10.1 𝑓𝑒𝑒𝑡 × ? 𝑓𝑒𝑒𝑡 2 72.8 𝑓𝑒𝑒𝑡 2 = 10.1 𝑓𝑒𝑒𝑡 × ? 𝑓𝑒𝑒𝑡 72.8 𝑓𝑒𝑒𝑡 2 = ? 𝑓𝑒𝑒𝑡 10.1 𝑓𝑒𝑒𝑡 7.2 𝑓𝑒𝑒𝑡 = ? 𝑓𝑒𝑒𝑡 Example 3: Find the area 𝐴𝑟𝑒𝑎 = 𝑠𝑖𝑑𝑒 2 𝐴𝑟𝑒𝑎 = (7.3 𝑓𝑒𝑒𝑡)2 𝐴𝑟𝑒𝑎 = 53.29 𝑓𝑒𝑒𝑡 2 Example 4: Find the area 𝐴𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 𝐴𝑟𝑒𝑎 = 6 𝑐𝑚 × 11.5 𝑐𝑚 𝐴𝑟𝑒𝑎 = 69 𝑐𝑚2 Example 5: Find the missing information 𝐴𝑟𝑒𝑎 = 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ 6𝑓𝑡 2 = 3 𝑓𝑡 × ? 𝑓𝑡 6 𝑓𝑡 2 =? 𝑓𝑡 3 𝑓𝑡 2 𝑓𝑡 = ? 𝑓𝑡 Homework ASSIGNMENT 10-1