# math

posted by .

Hello,

Here is a question with something i've never heard of.

These are the first two stages of a fractal known as the Sierpinski carpet. The carpet begins with a square (stage 1). The square is cut into 9 congruent squares and the middle square is removed (stage 2).

Draw stage 3 using the method described to get from stage 1 to stage 2.

To the nearest whole percent, what percent of the original square remains in stage 3? Show your work and explain your answer.

• math -

ok, I realize that I should cut each remaining square into 9 quadrants leaving the middle open of each of them.

Now, I just don't know how to get the percent of the original square that remains in stage 3.

• math -

In stage one say the square is 9 units by 9 units thus 81 square units in area.

Then we cut it into 9 units each 3 units by three units so each 9 square units in area. We remove one so we only have 8 left each 9 square units in area.

Now for stage 3 we split each of those 8 squares into 9 squares each one unit by one unit or one unit square. We now divide one of those 1 by 1 squares into 9 squares each 1/3 by 1/3 so we can remove the middle one. The area left is 1 minus the middle which is 1/3*1/3 = 1/9 so it is 8/9

so we started with a square of 9 by 9 or 81 square units and now we have a little square with area of 8/9 square units so
(8/9)/81 is the ratio of area of one of the final little carpets to the original carpet.

• math -

Remember you have 8 of those little carpets.

• math -

This might help, nice drawing of it.

## Similar Questions

1. ### math

Ok The Galtins are buying a carpet for their home. They need about 1,175 square feet of carpet. The carpet they buy is sold by the square feet. What is the estimate of number of yards the Galtins need for thier home?
2. ### math

A simple fractal tree Grows in stages. A each new stage, two new line segments branch out from each segment at the top of the tree. The first five stages are shown. How many line segments need to be drawn to create stage 20?
3. ### Math

Carpet plus installs carpet for \$100 plus \$8 per square yard of carpet. Carpet World charges \$75 for installation and \$10 per square yard of carpet. Find the number of square yards of carpet for which the cost including carpet and …
4. ### Math

Mr. Carpenter sent his wife to the store to buy 200 square feet (A) of carpet, but he forgot to tell her the length (L) and width (W) of the carpet (A=L*W). How many different sizes of carpet can she get and still have 200 square feet …
5. ### geometry

you plan to carpet 468ft of space. carpet costs \$26.75 per square yard and the tax is 7%. the carpet is sold in 12 ft rolls. what is the cost of the carpet?
6. ### Math

LeAnn is a carpet layer. She has agreed to carpet a house for \$18 per square yard. The carpet will cost her \$11 per square yard, and she knows that there is approximately 12% waste in cutting and matching. If she plans to make a profit …
7. ### math

4. Suppose your living room is a rectangle measuring 13 feet by 21 feet and it needs new carpet. How much carpet do you need in square yards and how much would your cost be if it is sold at \$21 per square yard?
8. ### maths

The Park's are buying new carpet for their house.They need about 1,175 square feet of carpet.The carpet they buy is sold by the square yard. Estimate the number of square yards of carpet the Parks need for their house. Show your work.
9. ### math

A piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide. What is the area of the reduced carpet?
10. ### math

Each side of a square classroom is 9 yards long. The school wants to replace the carpet in the classroom with new carpet that costs \$88.02 per square yard. How much will the new carpet cost?

More Similar Questions