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1.7: Various Formulas, Part 1 Objectives: 1. To use formulas to find the perimeter, circumference, and area of squares, rectangles, triangles, and circles Assignment: • 1.7 Various Formulas Worksheet: 1-20 Objective 1 You will be able to use formulas to find the perimeter, circumference, and area of squares, rectangles, triangles, and circles Units vs. Square Units The length of something (a segment, a room, a board) is measured in units: inches, feet, centimeters, meters, etc. It’s a one-dimensional measurement. 1 Length: 1 unit Perimeter The perimeter of a polygon is the sum of lengths of all the segments that make up the polygon. It is basically the distance around the shape. 5.35 cm 4.82 cm 3.72 cm 6.04 cm 4.30 cm Perimeter = 5.35 + 4.82 + 6.04 + 4.30 +3.72 = 24.23 cm Let’s Have Some π The distance around a circle is its circumference. Circumference Diameter Units vs. Square Units The area of something (a polygon, a floor, a wall) is measured in square units: in2, ft2, cm2, m2, etc. It’s a twodimensional measurement. 1 1 Area: 1 square unit Area The area of a plane figure is the measure, in square units, of the region enclosed by the figure. This is simply the number of unit squares that can be arranged to completely cover the figure. If two polygons are congruent, what do you suppose is true about their areas? Formula City Exercise 1 Find the area and perimeter (or circumference) of each figure. Exercise 3 The Large Hadron Collider is a circular tunnel that spans a 27 km circumference. What is the diameter of the LHC ring? Exercise 4 If the irrigated circular field shown has an area of 804.25 m2, what is the length of the rotating sprinkler (the radius of the circle)? Exercise 5 Find the area of the figure shown. Exercise 6 Given any of the previous formulas, what would it mean to solve for a particular variable? To solve for a variable in an equation or formula means to isolate that variable on only one side of the equation: variable = everything else Exercise 7 1. Solve 𝐶 = 2𝜋𝑟 for 𝑟. Then find the radius of a circle with a circumference of 44 in. 4 𝜋𝑟 3 3 2. Solve 𝑉 = for 𝑟. Then find the radius of a sphere with a volume of 36 cm3. Exercise 8 Sometimes the variable you are solving for is part of an expression. 1. Solve 𝑃 = 2𝑙 + 2𝑤 for 𝑙. Then find the length of the rectangle whose perimeter is 30 in. and whose width is 7 in. 2. Solve 𝐴 = 1 (𝑏1 2 + 𝑏2 )ℎ for 𝑏1 . Exercise 9 Write a formula for the area of a circle in terms of its circumference. Then find the area of a circle with a circumference of 12.5 cm. 1.7: Various Formulas, Part 1 Objectives: 1. To use formulas to find the perimeter, circumference, and area of squares, rectangles, triangles, and circles Assignment: • 1.7 Various Formulas Worksheet: 1-20