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Area of Polygons (Using Decomposition)
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What you will learn from this videoWhat you will learn
- 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!
- Discussion Questions
Before Video
What is area?ANSWERArea 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 Video
How is the area of a right triangle related to the area of a rectangle?ANSWERThe 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.
- 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
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide