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Area and Perimeter of Rectangles Keystone Geometry

Area and Perimeter of Rectangles Keystone Geometry. h. b. h. b. Area Terminology. A base segment is any side of a polygon . A height segment is a segment that is perpendicular to a base segment , with one endpoint on the base & the other on the opposite side. h. b.

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Area and Perimeter of Rectangles Keystone Geometry

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  1. Area and Perimeterof RectanglesKeystone Geometry

  2. h b h b Area Terminology A base segmentis any side of a polygon. A height segmentis a segment that is perpendicular to a base segment, with one endpoint on the base & the other on the opposite side.

  3. h b Area of a Rectangle Rectangle Area: The area of a rectangle is the product of its base & height. (A = bh) A(rectangle) = bh

  4. A(square) = s2 s Area of a Square Area of Square: The area of a square is the square of the length of a side.

  5. Perimeter of Rectangles and Squares Perimeter: The distance around a 2 dimensional (flat) shape. Perimeter of a Rectangle P(rectangle) = b + h + b + h OR P(rectangle) = 2b + 2h Perimeter of a Square P(square) = s + s + s + s OR P(square) = 4s

  6. II I Area of combined figures Area Congruence Postulate: If 2 polygons are congruent, then they have the same area. Area Addition Postulate: The area of a region is the sum of the areas of its non-overlapping parts. NOTE! Figures can often be divided in multiple ways, divide the shape into whatever appears easiest. A(figure) = A(I) + A(II)

  7. 15 x 12 Example 1 Example 1: The base of a rectangle is 12 cm; it has a diagonal of length 15cm. Find the area and perimeter of the rectangle. A = bh what is missing? The height! A = 12x A = 12(9) to find height use the Pythagorean Theorem (3-4-5 triangle) A = 108 cm2 P = 12 + 9 + 12 + 9 = 42 cm

  8. A = 108 b Example 2 Example 2: The area of a rectangle is 108 units squared. If the height is 7.2 units, find the base. 7.2 A = bh 108 = 7.2b

  9. 12 5 8 2 Example 3 Example 3: Find the area and perimeter of the concave hexagon. (Hint: Find each individual area and then add them together) A(I) = bh = 12(5) = 60 A(II) = bh = 2(3) = 6 I 10 3 II Total Area = A(I) + A(II) = 60 + 6 = 66 sq. units Perimeter = 8+12+5+10+3+2 = 40 units

  10. 5 7 7 6 6 5 5 2 2 5 Total Area Examples Consecutive sides of the figures are perpendicular. Find the area of each figure. 1. 2. 2.8 2.8 2 2.8 2 2.8 2 2

  11. s h b II I Summary Area of Square: A(square) = s2 Perimeter of Square = 4s Area Congruence: If 2 polygons are congruent, then they have the same area. A(figure) = A(I) + A(II) Area Addition Postulate: Area of Rectangle: A(rectangle) = bh Perimeter of Rectangle = 2b+2h

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