Question - Calculating Cost of Siding for Cottage Ends
Solution:
To solve this question, we need to calculate the total area that needs to be covered with siding on one end of the cottage and then determine the total cost to put siding on both ends.The end of the cottage is in the shape of a triangle on top of a rectangle. We need to calculate the area of both and sum them up to get the total area for one end. Then, since there are two ends to the cottage, we'll multiply by 2.1. Calculate the area of the rectangle: $$ Area_{rectangle} = Width \times Height $$ $$ Area_{rectangle} = 28 \text{ ft} \times 8.5 \text{ ft} $$ $$ Area_{rectangle} = 238 \text{ ft}^2 $$2. Calculate the area of the triangle: The triangle's base is the same as the width of the rectangle, which is 28 feet. The height of the triangle (altitude) is from the top of the rectangle to the apex of the triangle, which is 12.5 feet. $$ Area_{triangle} = \frac{1}{2} \times Base \times Height $$ $$ Area_{triangle} = \frac{1}{2} \times 28 \text{ ft} \times 12.5 \text{ ft} $$ $$ Area_{triangle} = 175 \text{ ft}^2 $$3. Calculate the total area for one end: $$ Total Area_{one end} = Area_{rectangle} + Area_{triangle} $$ $$ Total Area_{one end} = 238 \text{ ft}^2 + 175 \text{ ft}^2 $$ $$ Total Area_{one end} = 413 \text{ ft}^2 $$4. Since both ends of the cottage are the same, we need to cover: $$ Total Area_{both ends} = Total Area_{one end} \times 2 $$ $$ Total Area_{both ends} = 413 \text{ ft}^2 \times 2 $$ $$ Total Area_{both ends} = 826 \text{ ft}^2 $$5. Finally, calculate the total cost. Each bundle covers 100 square feet and costs $75. First, find out how many bundles are needed: We have a total of 826 square feet, and each bundle covers 100 square feet, so we divide the total area by the area covered by one bundle: $$ Number of bundles = Total Area_{both ends} / Area_{per bundle} $$ $$ Number of bundles = 826 \text{ ft}^2 / 100 \text{ ft}^2 $$ $$ Number of bundles = 8.26 $$ Since we can't buy a fraction of a bundle, we round up to the nearest whole number, which means we need 9 bundles. Now, calculate the cost: $$ Total Cost = Number of bundles \times Cost per bundle $$ $$ Total Cost = 9 \times 75 $$ $$ Total Cost = $675 $$Therefore, the total cost to put siding on both ends of the cottage is $675.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com