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Areas of Polygons & Circle

Areas of Polygons & Circle. Geometry Lesson 2 (2 nd OP). Area Postulate. To every polygonal region, there corresponds a unique positive number called the area of the region . Area of the polygonal region refers to the number of square units that exactly fill it. 2. 4. 1. 3. 1. 2.

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Areas of Polygons & Circle

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  1. Areas of Polygons & Circle Geometry Lesson 2 (2nd OP)

  2. Area Postulate • To every polygonal region, there corresponds a unique positive number called the area of the region. • Area of the polygonal region refers to the number of square units that exactly fill it. 2 4 1 3 1 2 3 4

  3. SQUARE FACTS: • All sides are equal. • All angles are equal to 90 degrees. s A = s2 s

  4. A = s2 • If s = 5 units If s = 1 /2 inches • If s = 3.5 units If s = 2/3 inches • If s = 7 inches If s = √5 dm • If s = 15 cm If s = (x+2)

  5. RECTANGLE FACTS: • 2 parallel sides • Length and width • All angles are equal to 90 degrees w A =Lw L L w

  6. A =Lw • l= 5 units ; w= 2 units • l= 3.5 units ; w= 2.2 units • I= 7 in ; w= 4 in • l= 15 cm ; w= 3 2/3 cm • l=1/2 m ; w= 1/3 m • l=√25 dm ; w= √4 dm • l=√10 dm ; w= √5 dm • l=2√x in ; w= √x in • I= (x+2) ; w= (x+1)

  7. PARALLELOGRAM FACTS: • 2 parallel sides • Length/base and altitude/height (width of the rectangle) b A =bw h h a

  8. A =Lh • l= 15 cm ; w= 3 2/3 cm • l=1/2 m ; w= 1/3 m • l=√16 dm ; w= √2.5 dm • l=2√3 dm ; w= √3 dm • l=2√x in ; w= √2x in • I= (x+5) ; w= (x-2)

  9. TRIANGLE h h L(base) L(base) A =bh A =bh A =bh 2

  10. A =bh 2 FIND THE AREA OF THE TRIANGLE: • b=4; h=6 • b=12 ; h=3 • b=(2x+5) cm; h= 5 cm b=(4x-5) in; h=(4x+5) in

  11. A =bh 2 • If height(a) or base(b) is unknown(x), given the third side (hypotenuse). • [only for right Δs] • Pythagorean Theorem • c2 = a2 + b2 • Trigonometric Functions • SOH, CAH, TOA • CHO, SHA, CAO

  12. 45-45-90 special right Δ • If a=1, b=____, • h=____; A= • If b=2, a=____, • h=____; A= • If a=3, b=____, • h=____; A= • If h=10√2, • a=____,b=____ • A=____ • If h= 23√2, • b=___,a=____ • A=_____ 45 h (n√2) a (a=b) (n) 45 b (b=a) (n)

  13. 30-60-90 special right Δ • If a=√3, b=____, • h=____; A=_____ • If b=2, a=____, • h=____ ; A=_____ • If a=3√3, b=____, • h=____; A=_____ • If h=10,a=____, • b=____; A=_____ • If h= 20,b=____, • a=____; A=_____ 30 h a (2n) (n√3) 60 b (n)

  14. Equilateral Triangle • All sides are equal • All angles are equal – 60 degrees AEq=s2√3 4 FACTS

  15. AEq=s2√3 4 • If s=3 , A=_____ • If s=2.5 cm, A= _____ • If s=12, A=______ • If s=200 ½ mm, A= _____ • If s=11√4 m, A= _____ • If s=4x in, A= ______ • If s=(2x+2) m, A= _____ • If s=(6x3-4y) in, A= ______

  16. TRAPEZOID FACTS: • 2 bases (b1 and b2) that are parallel. • Leg/s • height BASE LEG LEG A =(b1+b2)h 2 h A =bh 2 BASE

  17. A =(b1+b2)h 2 • If b1=5 cm, b2= 10 cm, h=5 cm, A=_______ • If b1= 4x, b2= 12x, h=2x, A=_________ • If b1=(2x+1) in, b2=(x-1) in, h=10 in, A=___

  18. RHOMBUS A=1/2 d1d2 • FACTS: • 4-sided polygon with all sides equal. • No angle is equal to 90 degrees. d2 d2 d1 d1

  19. A=1/2 d1d2 • If a=3, b=4, A=____ • If a=4 m, b=8, A= _____ • If a=(2z) in, b=(4z) in, A=______ • If a=6 in, c=12 in, A=______ • If a=2, c=6 ,A=______ • If b=4, c=12, A=______ • If b=8, c=24, A=_______ c a b

  20. Area of a CIRCLE Aʘ=Πr2 • From parallelogram: • A = bh • = ½ C (r) • = ½ (2Πr)(r) To circle: • A= Πr2 r

  21. Aʘ=Πr2 • r=2.5 cm, Aʘ=_______ • r=√5 cm, Aʘ=_______ • r=7√2cm, Aʘ=_______ • d=16 mm, Aʘ=_______ • d=18 in, Aʘ=_______ • d=20√4 cm, Aʘ=_______

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