unit 1.3 - measuring line segments using squares
what do we need to know?
- The area of a triangle: (Base x Height)/2
- The area of a square: Base x Height
- The area of a "bigger" shape is equal to the sum of the areas of all the shapes that make up said shape.
- The area of a square: Base x Height
- The area of a "bigger" shape is equal to the sum of the areas of all the shapes that make up said shape.
class notes
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MORE information
To measure line segments in this part of the unit, we will use two types of squares (all within a grid).
1. A square which corners are perfectly lined up:
1. A square which corners are perfectly lined up:
2. A square which corners do not lined-up (tilted):
The two methods to measure the square's side length
the "inside" Method
- Figure out all the shapes inside the square.
- Calculate the area of each of those shapes.
- Add all the areas together.
- Once you have the greater area, remember that:
- Calculate the area of each of those shapes.
- Add all the areas together.
- Once you have the greater area, remember that:
lined-up corners
Look at this example:
- As you can see, this type of squares is made up of 4 IDENTICAL TRIANGLES.
- That means, the area of the square is equal to the area of 4 triangles added together.
- The area of ONE TRIANGLE = (Base x Height) / 2 = (5 x 5) / 2 = 12.5 units square. Each of the triangles has an area of 12.5 units square
- The area of the square = 4 x (area of one triangle) = 4 x 12.5 = 50 units square.
So, the area of the square is 50 UNITS SQUARE
and the side length is:
- That means, the area of the square is equal to the area of 4 triangles added together.
- The area of ONE TRIANGLE = (Base x Height) / 2 = (5 x 5) / 2 = 12.5 units square. Each of the triangles has an area of 12.5 units square
- The area of the square = 4 x (area of one triangle) = 4 x 12.5 = 50 units square.
So, the area of the square is 50 UNITS SQUARE
and the side length is:
non-lined up corners
- From each of the corners, project and draw a line towards the middle until that lines intercepts another line. - When you do this, you'll notice that the inside of this square is made up of one smaller square in the middle, and four triangles. - Calculate the area of the smaller middle square. - In this example, the area is = Base x Height = 4 x 4 = 16 units squared - Notice that the 4 triangles inside the square are identical. - If we calculate the area of 1 triangle, and multiply it times 4, we will get the total triangular area. - Area of one triangle = (Base x Height)/2 = (3 x 7)/2 = 21 / 2 = 10.5 units squared. - Thus, the TOTAL triangular area is = (10.5 units squared) x 4 = 42 units squared - Now that we have the areas of all the shapes inside the big square, all we need to do is add them all together. - Total Area = Area of smaller square + Area of 4 triangles = 16 units squared + 42 units squared = 58 units squared |
The side length of this square is:
The "outside" method
THIS METHOD CAN ONLY BE USED WHEN THE SQUARE HAS ALL CORNERS LINED UP!!!
- As it works out, the area of a lined-up square inside a grid is equal to the sum of the area of the 4 triangles in the outside corners.
- These triangles are identical to one another.
- To calculate the area, get the area of one triangle and multiply it times 4.
- These triangles are identical to one another.
- To calculate the area, get the area of one triangle and multiply it times 4.
videos that may help
Online EXTRA INFORMATION
1-3powerpointnotes.ppt | |
File Size: | 1227 kb |
File Type: | ppt |
worksheets
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review - workbook
math_8_-_unit_1.3.pdf | |
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