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 Need 2 sides & an included angle… let’s find stuff 180 – 56.9 – 71.4 = 51.7 46.7 52.835 e E F D 56.9°51.7° K = 968 cm 2 e = 52.835 71.4°

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 15 11 want this altitude… use K = ½bh 9.3 = h 9.3 in

5. 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

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

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

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

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 cm 2 24) 18 times larger