Exploring Area and Perimeter

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Slide 1:

Geometry Exploring Area and Perimeter

Slide 2:

What You'll Learn Why You Should Learn It How to find the perimeter of a polygon How to find the area of a square and rectangle You can use perimeters and areas to solve real-life problems, such as finding the amount of fertilizer to cover a lawn

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Perimeter The perimeter of a polygon is the sum of the length of its sides Linear Measurement (cm, m, in, ft, mi, etc.)

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Example 1 Use a compass and straightedge to construct a segment whose length is equal to the perimeter of PQRS

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Example 1 Draw a long segment Use your compass to measure each segment P Q R S P PQ + QR + RS + SP = Perimeter of PQRS

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Areas of Squares & Rectangles Area of a polygon is the number of square units contained in its interior Areas are measured in square units such as m 2 or ft 2 3 3 1 2 3 4 5 6 7 8 9 9 units 2

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All formulas for areas of polygons based on these 3 postulates Postulate 22 - Area of a Square Postulate : The area of a square is the square of the length of its side, or A = s 2 Postulate 23 – Area Congruence Postulate : If two polygons are congruent, then they have the same area Postulate 24 – Area Addition Postulate: The area of a region is the sum of the areas of all its non-overlapping parts

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Theorem 11.1 Area of a Rectangle Theorem: The area of a rectangle is the product of its base and height, or A = bh The base and height meet at right angles h b

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Example 2 Each of the three rectangles has a height of 6 units and a base of 4 units. Each is composed of congruent polygons. Find the area of each polygon

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Example 2 Each of the three rectangles has a height of 6 units and a base of 4 units. Each is composed of congruent polygons. Find the area of each polygon 1 1 Twenty-four 1 unit by 1 unit squares 1 Square Unit Twelve 1 unit by 2 unit squares 1 2 2 Square Units Six congruent hexagons 24÷6 =4 4 Square Units

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Example 3 Comparing Perimeters and Areas of Squares Find a pattern for the perimeters and a pattern for the areas of the following squares. Graph your results and find functions that give the perimeter and area in terms of the side lengths

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Example 3 Begin by making a table that shows the perimeter and area of each square Side length, s 1 2 3 4 5 Perimeter, P Area, A

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Begin by making a table that shows the perimeter and area of each square Side length, s 1 2 3 4 5 Perimeter, P 4 8 12 16 20 Area, A 1 4 9 16 25 Example 3

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P = 4s A = s 2

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THE END

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