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

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## Finding the Area of a Basic Figure

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**Finding the Area of a Basic Figure**Developing the Area formulae for Squares, Rectangles, Parallelograms, Triangles, and Trapezoids. Square Triangle Parallelogram Rectangle Trapezoid**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**What is Area?**Since Area is measured in Square units we will start by defining the area of a unit square. 1 unit 1 unit The Area of this object is Defined as 1 unit2.**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 4 units The Area of this object is 16 units2.**The Area of a Square**Following the pattern for any Square we can develop a formula S units S units The Area of this object is S*S units2 or S2 units2**The Area of a Square**SO….The Area of any square is: Area = S2 (Where S is the length of the sides of the Square) S units S units**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 units2.**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 units2.**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**The Area of a Parallelogram**To Find the Area Formula for Parallelograms we must slice it and turn it into a Rectangle Height Base**The Area of a Parallelogram**Start by identifying a line of height perpendicular to the base. Height Base**The Area of a Parallelogram**Cut the Parallelogram along the height and move half the shape to the other side. Height Base Height Base**The Area of a Parallelogram**Notice that the shape turned into a Parallelogram with the same Height and Base Height Base Height Base**The Area of a Parallelogram**SO…the are formula for a Parallelogram IS identical to the Area formula for a Rectangle. Height Base Height Area = b*h Where b is the base and h is the height Base**Parallelogram Example**8 10 Area = b*h = 10*8 = 80 units2**The Area of a Triangle**Again the goal is to turn the triangle into a shape we already know Height Base**The Area of a Triangle**Start by Copying the Triangle Height Base**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.**The Area of a Triangle**Since the original triangle is half of the Parallelogram, then the area is also half. Height Base Area = (Area of Parallelogram) = b*h**Triangle Example**4 6 Area = = *4 = 12 units2**The Area of a Trapezoid**Again the goal is to turn the trapezoid into a shape we already know Base 1 Height Base 2**The Area of a Trapezoid**Like the triangle, copy the original trapezoid Height Base**The Area of a Trapezoid**Rotate the trapezoid and place it so one pair of legs overlap Base 1 Base 2 Height Base 1 Base 2 Notice: The new shape is a Parallelogram & the trapezoid was half of the new shape.**The Area of a Trapezoid**Since the Trapezoid is half the parallelogram: Base 1 Base 2 Height Base 1 Base 2 Area = b*h = *h**Trapezoid Example**5 4 8 Area =*h =*4 =(13)*4 = 6.5*4 = 26

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