GEOM HW3

HW 3 Name: __Ashtan Grumbles___ MATH 2160 Fall 2023 Submit all your work as a single PDF on Canvas under HW 3. Make sure that your work is clear and organized. You do not need to print this document or write the problems. Your work should include enough detail to demonstrate clear understanding of the mathematical concepts we are covering in class. 1. The figure below is a kite. The distance from I to K is 20 inches, the distance from I to T is 13 inches, and the distance from I to E is 24 inches. Determine the area of the kite using only the ideas discussed in class. Show all your work. Explain your reasoning. 2. A large running track is constructed to have straight sections and two semicircular sections with dimensions given in the figure below. Assume that runners always run on the inside line of their lane. A race consists of one full counterclockwise revolution around the track plus an extra portion of straight segment, to end up at the finish line shown. What should the distance x between the two starting blocks be in order to make a fair race? Explain your reasoning. 1 1 2 ( 12 ) ( 16 ) = 96 1 2 ( 12 ) ( 5 ) = 30 96x2=192 30x2=60 192+60=252in ,l a 2 + b 2 = c 2 12 12 +b 2 =13 2 144+b 2 =169 B 2 =169-144 B 2= √ 25 B=5 a 2 + b 2 = c 2 a 2 + 12 2 = 20 2 a 2 =20 2 -12 2 a 2 =400-144 a 2 = √ 256 A= 16 212 24 in. 2(3.14)(40)=251.2 2(3.14)(45)=282.6 251.2+200=451.2 282.6+200=482.6 482.6-451.2= 31.4

HW 3 Name: ________________________ MATH 2160 Fall 2023 3. The Browns plan to build a 6-foot-wide garden path around a circular garden of diameter 34 feet, as shown in the figure below. What is the area of the garden path? Explain your answer. 4. You are baking a round 24-inch pizza. a. What are the dimensions of the smallest rectangular baking sheet that you can use to bake the pizza? (The pizza should fit in the baking sheet without being folded, cut, or its shape being modified in any way.) 24x24 b. How much area of the baking sheet is not used when the round 24-inch pizza is been baked? 2 3.14(23) 2 3.14(529)=1,661.06 3.14(17) 2 3.149(289)=907.46 1,661.06-907.46=753.6 f Area of the pizza: 3.14(12) 2 =452.16 Area of the pan: 24x24=576 576-452.16= 123.84in 24 inches

HW 3 Name: ________________________ MATH 2160 Fall 2023 7. Given a right triangle with short sides of lengths a and b and hypotenuse of length c , use the figures below to explain why ? 2 +? 2 =? 2 . (You may assume that all shapes that look like squares really are squares and that, in each picture, all four triangles with side lengths a, b, c are identical right triangles.) Since there are 4 triangles you would use the formula for area of a triangle, 4 ( 1 2 ba ) . Then would add that to the area of a square, (bxh) ,for the green square which would be b 2 add that to the area of the orange square a 2 . That would make the equation 4 ( 1 2 ba ) + b 2 + a 2 you would then set that equal to the other figure. Since there are 4 triangles again use that same formula of 4 ( 1 2 ba ) and add C 2 for the area of the orange square. Now the equation is 4 ( 1 2 ba ) + b 2 + a 2 = 4 ( 1 2 ba ) + c 2 . Next you would subtract one side of the triangle formula from the other so they cancel out, then that leaves you with a 2 + b 2 = c 2 4

HW 3 Name: ________________________ MATH 2160 Fall 2023 5