Area of a Triangle

Area Of A Triangle REMINDER Area Of Triangle =½(base x height) A B C D c a h b For triangle BCD, sinC = h a h = asinC

So, for triangle ABC, Area Of Triangle =½(base x height) Area Of Triangle = ½(b x asinC) Area Of Triangle = ½basinC Area = ½absinC Area = ½acsinB Area = ½bcsinA

Example 1 Calculate the area of the triangle shown. 80 o AB C 24cm 19cm Area = ½bcsinA Area = ½(19)(24)sin80 o Area = 224.5cm 2, to1dp

Calculate the area of the triangle shown. Example 2 P Q R 41 o 21m 16.2m 15m Area = ½prsinQ Area = ½(16.2)(21)sin41 o Area = 111.6m 2, to 1dp

Example 3 Calculate the area of the shape below. AB CD 80 o 102 o 120m 110m 80m 108m Triangle ABC A = ½acsinB A = ½(110)(120)sin80 o A = m 2, to 1dp Triangle ADC A = ½acsinD A = ½(80)(108)sin102 o A = m 2, to 1dp TOTAL AREA = m 2, to 1dp

Example 4 The area of the triangle below is 60cm 2. Calculate the size of the acute angle XZY, correct to 3 significant figures. X Y Z 14cm 18cm A = ½xysinZ 60 = ½(14)(18)sinZ 60 = 126sinZ sinZ =  Z = )( sin -1  XZY = 28.4 o, to 3 sf