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5.5 Area of a Triangle

5.5 Area of a Triangle. From Geometry, we know the area formula for a triangle is A = ½ bh But there are other ways too! Area of a triangle K . OR. where semiperimeter s = ½(a + b + c). Ex 1) Find area of △ DEF if m ∠ D = 56.9 ° , m ∠ E = 71.4°, d = 46.7 cm. E.

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5.5 Area of a Triangle

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  1. 5.5 Area of a Triangle

  2. From Geometry, we know the area formula for a triangle is A = ½bh But there are other ways too! Area of a triangle K OR where semiperimeter s = ½(a + b + c)

  3. Ex 1) Find area of △DEF if m∠D = 56.9°, m∠E = 71.4°, d = 46.7 cm E Need 2 sides & an included angle… let’s find stuff 180 – 56.9 – 71.4 = 51.7 71.4° 46.7 56.9° 51.7° F D e 52.835 K = 968 cm2 e = 52.835

  4. Ex 2) A triangular sign with side measures of 11, 13, and 15 in. requires a brace perpendicular to the longest side from the opposite vertex. Determine the length of the brace. (We will use two separate formulas for area!) 13 11 15 want this altitude … use K = ½bh 9.3 in 9.3 = h

  5. We can also add or subtract areas of various shapes. Reminders for Area: • square • equilateral △ • circle • sector (θ in rads) OR (x is central angle in degrees) (from Geometry) *Hint: Draw a “plan” for what you want to add or subtract!

  6. Ex 3) Determine area of the shaded region. 118° 44 44 Sector – Triangle 1993.585 – 854.693 1138.892

  7. Ex 4) Determine area of the polygon. 17.4 13.9 x 41° 11.578 11.2 8.7 Use law of cosines to get x x = 11.578

  8. Ex 4) Determine area of the polygon. 17.4 There are lots of other regions to find area of, but these examples should be enough guidance! x 13.9 41° 11.578 I II 11.2 8.7 △I  = 63.928 △II  = 50.194 = 114.122 Total Area = 63.928 + 50.194

  9. Homework #505 Pg 276 #1, 3, 5, 11, 15, 22, 24, 29, 31, 35, 39, 41, 47, 51 Answers to Evens: 22) 439.8 cm2 24) 18 times larger

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