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Area of Polygons (Using Decomposition)

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- We'll learn to find the area of polygons by decomposing shapes.
- We will also learn how to find the area of polygons displayed on a coordinate plane.
- And we will see how this knowledge helps people create video games, build houses and even skateboard ramps!
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Discussion Questions
- Before VideoWhat is area?ANSWER
Area is a measure of the space inside a 2D object.
I can measure the sides of the rectangle, and then find the area using the formula length times width.
I can break the shape into two rectangles. I can find the area of each rectangle and add the areas together to find the area of the bigger shape.
I can draw lines to break a rectangle into other rectangles, squares, triangles, and other polygons.
The total area of all of the shapes is equal to the area of the original rectangle.
- After VideoHow is the area of a right triangle related to the area of a rectangle?ANSWER
The area of a right triangle is half the area of a rectangle with the same base and height.
I can break a parallelogram into two identical right triangles and a rectangle. When I combine the two triangles it forms a new rectangle. The area of this set of shapes is the same as the area of a rectangle with a length and width the same as the length and height of the parallelogram.
I can divide a polygon into rectangles and right triangles. Then I can find the area of each of the smaller shapes and add them together to find the total area.
First I plot each point. The coordinates tell me the position of the point on the x-axis and the y-axis. After I plot each point, I connect the points to make a polygon. I need to connect the points with straight lines and make a closed shape.
I can find the area in the same way, by dividing the shape into rectangles and triangles and finding the total area of those shapes.
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Vocabulary
- Area DEFINE
The measure of the space enclosed by the sides of a shape.
- Decompose (a shape) DEFINE
Breaking a shape into smaller shapes.
- Polygon DEFINE
A closed shape with straight sides.
- Rectangle DEFINE
A closed shape with 4 straight sides with 4 right angles.
- Triangle DEFINE
A closed shape with 3 straight sides.
- Right triangle DEFINE
A triangle where one angle measures 90 degrees.
- Parallelogram DEFINE
A closed shape with 4 straight sides. Two pairs of sides are parallel.
- Kite DEFINE
A closed shape with 4 straight sides. Two pairs of adjacent (next to each other) sides have the same length.
- Trapezoid DEFINE
A closed shape with 4 straight sides. At least one pair of sides are parallel.
- Area DEFINE
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Reading Material
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Practice Word Problems
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Practice Number Problems
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Lesson Plan
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Teacher Guide