Design a dance floor with a mosaic pattern.
• Classify triangles, use congruent triangles in real-life situations, find the areas of triangles and quadrilaterals.
Investigation: You work for a construction company. One of your clients wants the company to build a 16 foot by 20 foot dance floor. They want the floor to be a mosaic pattern made up of congruent triangles. Your boss wants you to design the floor and determine the cost. You spoke with the client and they agreed to let you use a few quadrilaterals in addition to the congruent triangles. However, they want the triangles to be at least 50% of the area of the design, they want at least 30 congruent triangles with at least two differently shaped triangles, and they want the largest dimensions of any of the quadrilateral to be no more than 3 feet by 3 feet. They understand the cost of the dance floor will be based on the shapes that you use.
Constructing the floor: You decide to model the floor design using an 8 inch by 10 inch piece of graph paper. Your workcanbeapproachedinseveralways. Twopossibilitiesaregivenhere:
1) You can draw a design on the graph paper and do the needed calculations to be sure you meet theclient’sspecifications. OR
2) You can cut the piece of graph paper into as many pieces as you want, using at least 50% of the paper for the triangles, and reassemble them to form an interesting pattern. The shapes need to be reassembled to form an 8 inch by 10 inch rectangle.
Determining the Cost: The client likes your design, but wants to be assured you followed their specifications. They agree to pay the flooring bill but will check it carefully to make sure it matches the design.
1) Make a table of all the shapes you used. For each shape include the quantity you used, the individual area, and the total area.
2) Provide additional calculations to convince the client that triangles cover at least 50% of the flooring.
3) Write an organized and detailed bill for the client. Include the amount of sales tax, 6.5%. The cost of the flooring is based on the shapes as follows:
$5.35 for any scalene triangle
$4.50 for rectangles
$3.75 for equilateral or isosceles triangles $4.00 for squares
$7.60 for any other quadrilateral
How do you think we can help you with this assignment?
Can you help me with how to draw fig and preparing the table of estimated cost
We can't draw figures here.
What about the instructions don't you understand?
To design the dance floor with a mosaic pattern, we need to follow the client's specifications and meet certain requirements such as using congruent triangles, having at least 30 congruent triangles with at least two differently shaped triangles, and ensuring that triangles cover at least 50% of the flooring.
First, let's approach the task by drawing a design on the graph paper and doing the necessary calculations. We have an 8 inch by 10 inch piece of graph paper to work with.
1) Start by dividing the graph paper into congruent triangles and quadrilaterals. Ensure that the triangles are at least 50% of the design. You can use different shapes and sizes of quadrilaterals, as long as they do not exceed the maximum dimensions of 3 feet by 3 feet.
2) Once you have divided the graph paper, count the number of each shape you used. Create a table to record this information. For each shape, include the quantity used, the individual area, and the total area.
3) To determine the cost, assign prices to each shape. Here are the prices for the different shapes:
- Sc