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Area of a Triangle 7.3. JMerrill, 2009. Area of a Triangle (Formula) . When the lengths of 2 sides of a triangle and the measure of the included angle are known, the triangle is uniquely determined. Use: S = ½ ab sin C S = ½ bc sin A S = ½ ac sin B.
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Area of a Triangle7.3 JMerrill, 2009
Area of a Triangle (Formula) • When the lengths of 2 sides of a triangle and the measure of the included angle are known, the triangle is uniquely determined. Use: • S = ½ ab sin C • S = ½ bc sin A • S = ½ ac sin B Do not memorize all the individual formulas, memorize the pattern: S = ½ (one side)(2nd side)(sine of incl. angle)
Example • Two sides of a triangle have lengths 7cm and 4cm. The angle between the sides measures 73o. Find the area of the triangle. • S = ½ (7)(4)sin 73o • S = 13.388cm2
You Do #1 • Given the triangle ABC with measures of b = 3, c = 8, <A = 120o, find the area: • 10.392units2
Find the area of a regular hexagon inscribed in a unit circle (means the radius is 1 unit). Then approximate the area to 3 significant digits. Example Flashback to geometry…what does “regular” mean? First, divide the hexagon into six congruent triangles.
Second, label the known quantities S=6(½)(1)(1)sin60 S=2.60 units2 Example 1 1 60o Where did the 6 come from?
You Do #2 • Find the area of a regular octagon inscribed in a circle with a radius of 20. Round to the nearest tenth. 1131.4 units2
Approximate the area of the irregularly-shaped piece of land (hint: split it into 2 triangles, one of which is a right triangle). All measurements are given in feet. Round to the nearest whole number. You Do: Challenge 16 110o 5 12 Area of right triangle: 30ft2 Length of drawn segment: 13ft Total area: 101ft2