Finding areas and squares

Today, we finished covering chapter 6 with section 6.4. We covered two concepts: finding the area of a shape and finding the square root of a number.

To learn the concept of finding the area, we looked at pictures of shapes on a geoboard. Every square that is within a shape is one square unit. So, to find the total area, you just have to count the number of squares within the shape.

9This square on a geoboard consists of 9 small squares, so the area is 9.

Some shapes are not as simple to find the area of, however. If half of a square is included, then you add a half to the total area. If the shape is a triangle, then you can find the area of two of those triangles, which would be a rectangle. Divide that area by 2 to get the area of the triangle.

triangleThe area of the rectangle is 2. Since the rectangle is twice the amount of the triangle, the area of one triangle is half of the rectangle. The area is 1.

If the shape is a square that is tilted, then you will have to use this same rectangle method to find the total area. To do this, first find the number of complete squares in the shape. Then make rectangles for all the triangles left on the shape.

squareThis shape does not have any complete squares in it. So, you just have to add the areas of the triangles in it. There are 4 triangles. The area for each one can be found by finding the area of the square that surrounds it. The area of the squares are 1 each, so each triangle’s area is 1/2. The total area of the shape would be 2.

Next, we learned that finding squares of numbers can be done by doing factor trees. So, if I wanted to find the square root of 24, I would make a factor tree for 24 first. It would look like this:

factor treeSo, the prime factorization for 24 is 2•3•2•2.

Next you would replace the 24 under the square root sign with this prime factorization. Any number that has a pair under the square root sign would be moved outside of it. Then you would combine the terms outside and inside the symbol. So it would look like this:

√24 = √2•3•2•2 = 2√3•2 = 2√6

To do the cubed root, you would still replace the number with its prime factorization. Instead of moving pairs of numbers out, you would move triples out from the symbol.

Watch this video for more examples of this.

Well, it looks like that’s it for my blogging project! I enjoyed this project, and it turned out to be a good way to review the material covered in class. Thanks for reading!!



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