5.5 Area of a Triangle. 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.

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Presentation transcript:

5.5 Area of a Triangle

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)

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

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!) want this altitude… use K = ½bh 9.3 = h 9.3 in

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

Ex 3) Determine area of the shaded region. Sector – Triangle – °

Ex 4) Determine area of the polygon. Use law of cosines to get x x = ° x

Ex 4) Determine area of the polygon. △ I  = ° x I II △ II  = Total Area = = There are lots of other regions to find area of, but these examples should be enough guidance!

Homework #505 Pg 276 #1, 3, 5, 11, 15, 22, 24, 29, 31, 35, 39, 41, 47, 51 Answers to Evens: 22) cm 2 24) 18 times larger