2.1+Finding+Areas+0910

JO**
 * 29/9/09
 * Big Idea**: The dimensions of a right triangle can be determined with limited information.
 * Essential Question:** how can I use square roots to find information about triangles?
 * Notes from class:** each square box equals a Unit square. There are many methods of finding the areas out. one of them is just add the squares up. But if there is a triangle, it would depend on how much square box it takes up. if it takes up a half, then it would equal 0.5


 * 2.1

A. The figures below appear on Labsheet 2.1. Find the area of each figure below

1.** 2 Unit squared
 * 2.** 1.5 Unit squared
 * 3.** 2 Unit squared
 * 4.** 4 Unit squared
 * 5.** 3 Unit squared
 * 6.** 4 Unit squared
 * 7.** 3.5 Unit squared
 * 8.** 6 Unit squared
 * 9.** 8.5 Unit squared
 * 10.** 8.5 Unit squared


 * B. Describe the strategies you used to find the areas

1.** I divided it into 2 squares and then added the two squares. 1+1
 * 2.** I divided it into 1 square and triangle and then I added the one square with the triangle which takes up half a square unit. 1+0.5
 * 3.** Each triangle equaled 1 since it was half of two unit squares. 1+1
 * 4.** I divided it into 3 squares and 2 triangles then i added the three squares and then added the two half a squared triangles. 1+1+1+.5+.5
 * 5.** I divided the rectangle into 4 triangles. Two half a squared triangles and 2 half a 2 squared triangles. 1+1+.5+.5
 * 6.** I divided it into 2 squares and 3 triangles. I first added the 2 squares and then added the 2 half squared triangles. Then i added the triangle which equals 1 since its half of 2 squares. 1+1+.5+.5+1
 * 7.** I divided it into 1 square and 3 triangles. Two of the triangles equaled 1 because it was half of 2 squares. And the other triangle was half of 1 square. And the rest i added it to the square. 1+1+.5+1
 * 8.** In this shape, i moved the little triangle on the right bottom to the side of the right. So then it would make 2 triangles. 1 facing up the other facing down. Then i would use the stradegy to find the area of the triangle. so for the first triangle i did, 4x2/2. The 4 is the length of the triangle and the 2 is the height of the triangle. And you divide it by two since thats how you find the area of a triangle. So it would equal 4. Do the same to the other one which is 2x2/2 which equals 2. Then add them together 4+2 and it would equal 6
 * 9.** I divided this into 4 squares and 6 triangles. I first added the 4 squares with 3 half squared triangles. then i added it with the triangle which equaled 1 since it was half of 2 squares. And the leftover two triangles, i had to use the method i used in 8. so it would be 2x1/2 for both of them since their the same size and it equaled 2 added them together which meant each was 1. So its 1+1+1+1+.5+.5+.5+1+1+1
 * 10.** I divided this into 5 squares and 4 triangles. I first added the squares up and then added it with two half squared triangles. then i added it with a triangle which equaled 1 since it was half 2 squares. Then i added it with a triangle which equaled 1.5 since it was half of 3 squares. so its 1+1+1+1+1+.5+.5+1+1.5


 * F.U

1. Find the area of each triangle below**


 * a.** 3 Unit squared
 * b.** 4 Unit squared
 * c.** 2 Unit squared
 * d.** 2 Unit squared
 * e.** 3.5 Unit squared
 * f.** 5 Unit squared


 * 2. Describe the strategies you used to find the areas**


 * a.** Since this is a triangle i did 3x2/2 (the same method as 8). which equaled 3
 * b.** 4x2/2=4
 * c.** For this i divided it into 2 triangles. 1 equaled 1.5 since it was half of 3 squares and the other equaled .5 since it was half of a square. 1.5+5
 * d.** 4x1/2=2
 * e.** For this triangle, since there wasn't any length, i made it inside a 4 by 4 square. I found the area of the square which was 16. Then there were 3 smaller triangles which had a length so it was easy to find the area for them. the first one was 3x4/2=6 the second one was also 3x4/2=6 and the last one was half of a square. so it was 6+6+.5 which equaled 12.5. Then i subtracted that by the big square to find the area of the triangle. So i did 16-12.5 which equaled 3.5
 * f.** I also put this triangle inside a square. the square equaled 12. and the three little triangles i did the same method. The first 1, 4x1/2=2 the second one, 3x2/2=3 and the third one, 2x2/2=2 so 2+3+2=7. 12-7=5