Characteristics of the Four Main Geometrical Figures


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1 Math & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle. (Note: There is no such thing as the perimeter of a circle, the distance around the outside of a circle is called the circumference.) Perimeter refers to the distance around the outside edges of an object. You do not need a formula for this quantity. You can always find the perimeter of an object by labeling all its sides, and adding up the outside edges. Area refers to the amount of space inside a flat (D) object. Characteristics of the Four Main Geometrical Figures Square Rectangle Triangle Circle 3.14 Perimeter Measures distance around outside edges Area Measures space inside an object Units Used ft, in, yds, mi, cm, m ft, in, yds, mi, cm, m Square s s s s 4s s l w l w lw Triangle Add up the 3 sides bh 1 bh Circle C D r called circumference Rectangle Math 40 1 of 6
2 Practicing the Eight Basic Computations 1. Find the perimeter and area for a square with sides of length 5 cm. P =. Find the perimeter and area for a rectangle with sides of length 5 in. and 1 ft. P = 3. Find the perimeter and area for a triangle with the following measurements: P = 4. Find the circumference and area for a circle with diameter 1 feet. Leave your answer in EXACT form. C = Answers: 1. P = 0 cm ; A = 5 cm. P = 34 in ; A = 60 in 3. P = 18 ; A = 8 4. C = 1π ft ; A = 36π ft Math 40 of 6
3 Circumference of a Circle Option 1: C D 1. Identify the Diameter. Attach the symbol, write it down 3. Adjust the units of your answer. Option : C r 1. Identify the radius. Double the radius 3. Attach the symbol, write it down 4. Adjust the units of your answer. Area of a Circle A r 1. Identify the radius. Square the radius 3. Attach the symbol, write it down 4. Adjust the units of your answer. Exact Answer Math 60 vs. Approximate Answer Math 0 Answer that is left in terms of. Example: 4 stays 4 Answer that is a numerical approximation, where a numerical value has been substituted for. Example: 4 gets replaced with (this is a numerical approximation to that has been rounded to the nearest hundredth) Notice how the approximations of 4 differ slightly depending on which value of we use. 4 4(3.14) = Use key on calculator (this uses a more accurate approximation to that is accurate to around 10 decimal places) 4 4( ) = = 1.57 (rounded to nearest hundredth) Math 40 3 of 6
4 Extra 9.7 & 9.8 Practice: These problems do not represent direct computations like the four previous problems they require you to think about the relationship between the quantities in order to obtain the answer. You do not need to have your work formatted in any particular manner, but put in whatever work you feel is necessary to arrive at the correct answer. 1. Find the area of a circle whose diameter is 18 feet.. Find the base of a triangle, if the height is 8 in and the area is 48 in. 3. Find the area of a rectangle with sides of lengths 8 inches and feet. 4. Find the length of the side of a square having perimeter 36 feet. 5. An isosceles triangle has two sides of the same length. Find the third side of an isosceles triangle with sides of length 4 inches where the perimeter is 10 inches. 6. If the circumference of a circle is 64π meters, what is the radius? 7. The area of a square is 36 ft. What is the length of one of its sides? 8. The perimeter of a rectangle is 4 feet. If the length is 7 feet, what is the width? Answers: 1. Area = 81π ft. Base = 1 inches 3. Area = 19 in 4. Side = 9 feet 5. Third Side = inches 6. Radius = 3 meters 7. Side = 6 feet 8. Width = 5 feet Math 40 4 of 6
5 Math 60 Level Geometric Problems: Solve the following physical situations. In order to receive full credit in Math 60 you would need to: Identify your variables through a let statement. Set up an algebraic equation that describes the physical situation. Solve your equation producing an algebraic solution. Answer the question being asked as a complete sentence. 1. A triangle has a perimeter of 74 inches. Find the three sides if one side is 4 inches larger than the smallest, and the third side is three times the smallest.. A slice of pie is in the shape of an isosceles triangle. If the shorter side is 8.5 inches less than twice the longer two sides, and the perimeter of the pie is 17.5 inches, determine the length of the shorter side. 3. The length of a rectangular patio is 4 feet greater than its width. If the perimeter is 11 feet, find the patio s dimensions. 4. A rectangular area is to be subdivided into three regions. Find the dimensions of this rectangle if the length is 40 feet greater than the width, and 560 feet of fencing is available to create this area. 5. A bookcase is to have three shelves, including the top. The height of the bookcase is to be 1 less than twice the width. Find the width and height of this bookcase if only 19 feet of lumber is available. Math 40 5 of 6
6 Quick Solutions for the Math 60 Level Geometric Problems # Algebraic Equation 1. x x 4 3x 74. x x x w w 4 w w w w w w w w 5. w w w w w Algebraic Solution Answer to the Question Asked x in., 34 in., and 30 in. x inches w 6 6 feet by 30 feet w feet by 10 feet x 3 3 feet by 5 feet The complete solutions for these five problems include: Let Statement Algebraic Equation Algebraic Solution Answer to the Question Being Asked and can be found online. The link is: Sections 9.5 & 9.6: Math 60 Geometric Problems Complete Solutions Note: The Math 60 Geometric Problems only involve computations for Perimeter which utilize Math 40 level equation solving skills. The skills necessary to solve equations involving Area are not developed until Math 60. Math 40 6 of 6
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