Althea’s family decided to attend the yearly sailing festival in their town. This year the boat races will include both rowing and sailing craft. Althea was excited about watching the racing events, as well as participating in the activities and seeing the informational booths for children. (Score for Question 1: ___ of 8 points) 1. Althea saw different types of sailboats on the water. She noticed that while each sailboat had triangular sails, different types of boats had different sizes and different numbers of sails. Here are two of the sailboats she saw: (a) What is the area of each sail? Which sailboat has the greatest total sail area? The area formula for a triangle is or . Show your work. (b) Althea wondered how much the material for a sail would cost. Nylon sailcloth costs $1.50 per square foot. What is the cost of the sails for each of the sailboats? Show your work. (c) Althea learned that a more expensive material for sails is carbon fiber. Carbon fiber costs 3 times as much as nylon sailcloth. What is the total price for carbon fiber sails for each boat? What is the difference in price between the catboat sail and the sloop sails when carbon fiber is used? Show your work. (d) Althea figured that if she tripled the length and doubled the width of the catboat sail, the price of the sailcloth would be 6 times as much because is 6. What is the area of the expanded sail for the catboat? What is the price of nylon sailcloth for this larger sail? Is Althea correct? Explain your reasoning.