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Finding the Area of a Basic Figure Developing the Area formulae for Squares, Rectangles, Parallelograms, Triangles, and Trapezoids. Square Parallelogram Triangle Rectangle Trapezoid

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What is Area? Area is a quantity that describes the amount a two- dimensional shape can cover a plane. Area is defined as the number of squares of a fixed size that cover the same space. Area can be thought of as the amount of material it can take to cover an object OR the amount of paint required to paint an object with a single coat

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What is Area? Since Area is measured in Square units we will start by defining the area of a unit square. 1 unit The Area of this object is Defined as 1 unit 2.

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The Area of a Square To find the area of a square we find how many unit squares fit into the actual square 4 units The Area of this object is 16 units 2.

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The Area of a Square Following the pattern for any Square we can develop a formula S units The Area of this object is S*S units 2 or S 2 units 2

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The Area of a Square SO….The Area of any square is: Area = S 2 (Where S is the length of the sides of the Square) S units

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The Area of a Rectangle We find the area of a rectangle similarly to how we found the area of a rectangle. 3 units 6 units The Area of this object is 6*3 = 18 units 2.

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The Area of a Rectangle Now we develop the formula by multiplying the number of columns (Base) with the number of rows (Height). Height Base The Area of this object is Base*Height = bh units 2.

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The Area of a Rectangle SO….The Area of any rectangle is: Area = b * h (Where b is the base and h is the height) Height Base

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The Area of a Parallelogram To Find the Area Formula for Parallelograms we must slice it and turn it into a Rectangle Height Base

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The Area of a Parallelogram Start by identifying a line of height perpendicular to the base. Height Base

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The Area of a Parallelogram Cut the Parallelogram along the height and move half the shape to the other side. Height Base Base Height

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The Area of a Parallelogram Notice that the shape turned into a Parallelogram with the same Height and Base Height Base Base Height

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The Area of a Parallelogram SO…the are formula for a Parallelogram IS identical to the Area formula for a Rectangle. Height Base Base Height Area = b * h Where b is the base and h is the height

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Parallelogram Example 8 10 Area = b * h = 10 * 8 = 80 units 2

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The Area of a Triangle Again the goal is to turn the triangle into a shape we already know Height Base

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The Area of a Triangle Start by Copying the Triangle Height Base

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The Area of a Triangle Rotate the copy and place it next to the original so that one pair of common sides overlap Height Base Notice: The new shape is a Parallelogram & the triangle was half of the new shape.

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The Area of a Triangle Since the original triangle is half of the Parallelogram, then the area is also half. Height Base

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Triangle Example 4 6

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The Area of a Trapezoid Again the goal is to turn the trapezoid into a shape we already know Height Base 2 Base 1

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The Area of a Trapezoid Like the triangle, copy the original trapezoid Height Base

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The Area of a Trapezoid Rotate the trapezoid and place it so one pair of legs overlap Height Base 2 Notice: The new shape is a Parallelogram & the trapezoid was half of the new shape. Base 1 Base 2

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The Area of a Trapezoid Since the Trapezoid is half the parallelogram: Height Base 2 Base 1 Base 2

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Trapezoid Example 4 8 5

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