A building owner has regulations for the business signs displayed on the front back of the building. In order to make the signs visible from the street, and the nearby freeway, the logo for each business sign must have the criteria shown.
• a maximum area of 40 ft.²
• a minimum width of 4 feet
Parkside printing hires a sign company to design a new logo for a sign which will hang on the building. The first two design submitted are shown.
Logo 1: radius= 1/2 scale: 1in=7ft
Logo 2: width 1/2 scale: 1in=6ft
In this task, you will answer some questions related to the building, regulations, criteria and designing sign logos to meet the regulations.
1. The chocolate shop has a rectangular logo for the business that measures 3 1/10 feet tall within an area that is exactly the maximum area allowed by the building owner. Create an equation that could be used to determine L, the unknown side length of the logo.
2. Now consider the logos for the Parkside printing shown determine the actual area of logo one in square feet.
3. Explain how to find the actual area of logo two. Then provide the area of logo two.
4. One of the logos meets the building requirements. Explain which logo meets the building requirements and why.
5. Parkside printing decides to select the logo you chose in question four. The business owner also wants to use a smaller version of the logo on the door of her business. The door is 7 feet tall and 3 feet wide. There should be 6 inches of empty space to the left side of the logo, and 6 inches of empty space to the right side of the logo. Based on the logo, selecting question four, what should be the total width, in feet, of the logo on the door? Enter your response in the first response box. Based on the logo, you selected in question four, what should be the total height, and feet, of the logo on the door?
1. Let L represent the unknown side length of the logo for the chocolate shop. The area of a rectangle is given by the formula A = L*W, where L is the length and W is the width. Since the area of the logo is given to be the maximum allowed area of 40 ft², the equation would be 40 = 3 1/10 * L.
2. To determine the actual area of logo one, we need to first calculate the length and width of the logo based on the scale given. Using the scale 1in=7ft, the width of the logo would be 4*7=28 ft. The radius of the logo is 1/2 scale, so it would be 1/2*7=3.5 ft. The area of a circle is given by the formula A = πr², so the area of logo one would be A = π*(3.5)² = π*12.25 ≈ 38.48 ft².
3. To find the actual area of logo two, we need to calculate the width of the logo based on the scale given. Using the scale 1in=6ft, the width of the logo would be 2*6=12 ft. The actual area of logo two would be A = 12*3 = 36 ft².
4. Logo two meets the building requirements because it has a width of 12 ft, which is greater than the minimum width of 4 ft required by the building owner.
5. Based on the logo selected in question four, the total width of the logo on the door should be 12 ft + 0.5 ft (6 inches on each side) + 0.5 ft (6 inches on each side) = 13 ft. The total height of the logo on the door would be 3.5 ft + 0.5 ft (6 inches on each side) = 4 ft.