Two-Dimensional Figures Polygons in .NET framework

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Two-Dimensional Figures Polygons
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A polygon is a closed, two-dimensional planar shape composed of a xed number of straight line segments Polygons are named according to the
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CHAP 7: MATHEMATICS
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number of sides they have Common examples include the triangle (3 sides), quadrilateral (4 sides), pentagon (5), hexagon (6), and octagon (8) Quadrilaterals include a parallelogram, rhombus, trapezoid, and square
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10 yds Irregular polygon P = 10 + 4 + 2 + 6 + 8 + 10 = 40 yds
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The perimeter of irregularly shaped polygons is calculated by just adding all the lengths of the sides
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s=2 Regular polygon (hexagon) P=n s P = 6 2ft = 12ft
The perimeter of regular polygons (all angles and all sides coincide [congruent]) is calculated by multiplying the number (n) of sides in the polygon by the length of a given side (s) The formula is: P = n s The area of different polygons is calculated using different formulas that are given below
PARALLELOGRAM
A parallelogram is a four-sided, two-dimensional gure that has two sets of opposite parallel sides The diagonals (straight line segments that cut across polygons joining two vertices, denoted in the diagram as d1 and d2) of a parallelogram bisect (cut in half) each other The perimeter of a parallelogram is calculated by adding the lengths of the four sides
PART III: REVIEW FOR THE WRITTEN EXAMINATION
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b Parallelogram b = 6 h = 4 A = (6 ) (4 ) = 24 inches2
The area of a parallelogram is the product of the base and the height The base (b) can be any side The sides perpendicular to the base are called the height (h) The area of a parallelogram can be calculated by using the formula: A=b h
RHOMBUS
A rhombus has a diamond shape It is a four-sided, two-dimensional gure in which all sides are of equal length and opposite sides are parallel
b Rhombus b = 6 cm h = 7 cm A = (6 cm) (7 cm) = 42 cm2
The perimeter of a rhombus is calculated using the same formula as used to get the perimeter of a regular polygon (P = n s) The area (A) of a rhombus can be calculated by multiplying the base (which can be any side) times the height (A = b h) or by nding half of the product of the lengths of its diagonals, A = 1/2 (d1 d2)
TRAPEZOID
A trapezoid is a four-sided, two-dimensional shape with two parallel sides The parallel sides of a trapezoid are called the bases (b1 and b2) The height of the trapezoid is the perpendicular distance between the bases (h)
CHAP 7: MATHEMATICS
h b1 Trapezoid b1 = 8 cm b2 = 6 cm h = 4 cm A = 4 cm (8 cm + 6 cm) = 4 cm (14 cm) = 2 cm (14 cm) = 28 cm2
The perimeter of a trapezoid is calculated by using the same formula as used to get the perimeter of a regular polygon (P = n s) The area (A) of a trapezoid is calculated by adding the lengths of the two bases, multiplying that by the height, and then dividing by 2 The formula is: 1 A = __ h (b1 + b2) 2
SQUARE
The square is a four-sided (polygon), two-dimensional shape with four equal length sides and four equal (right) interior angles The diagonals of a square __ are also equal to each other, perpendicular to each other and they are 2 (approximately 141) times the length of a side of a square
P=4xs A = s2 P = 4 x 3 = 12 A = (3 )2 = 9 inches2
The perimeter of a square whose sides have length (s) is calculated by multiplying any given side by 4 The formula is: P = 4 s The area of a square is calculated by raising any given side (s) to the second power The formula is: A = s2
RECTANGLE
A rectangle is a four-sided (polygon), two-dimensional shape where all four of its interior angles are 90 (right) angles The lengths of its diagonals are equal It has two pairs of opposite sides that are of equal length The length of the longer side is called the length (l) of the rectangle and the length of the shorter side is its width (w)
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