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 Do not memorize all the individual formulas, memorize the pattern: S = ½ (one side)(2 nd 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 = cm2

You Do #1 Given the triangle ABC with measures of b = 3, c = 8, <A = 120 o, find the area: Given the triangle ABC with measures of b = 3, c = 8, <A = 120 o, find the area: units units 2

Example 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. First, divide the hexagon into six congruent triangles. Flashback to geometry…what does “regular” mean?

Example Second, label the known quantities S=6(½)(1)(1)sin60 S=2.60 units2 Where did the 6 come from? o

You Do #2 Find the area of a regular octagon inscribed in a circle with a radius of 20. Round to the nearest tenth. Find the area of a regular octagon inscribed in a circle with a radius of 20. Round to the nearest tenth units 2

You Do: Challenge 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 o Area of right triangle: 30ft 2 Length of drawn segment: 13ft Total area: 101ft 2