Maths-
General
Easy

Question

Find the area of an isosceles triangle whose equal sides are of length 15 cm each and third side is 12 cm.

hintHint:

Use Heron’s formula

The correct answer is: 18√21 cm2


    It is given that a = 15 cm , b = 15 cm , c = 12 cm
    Using Heron’s formula,
    Area of triangle = square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root where s = fraction numerator a plus b plus c over denominator 2 end fraction
    s = fraction numerator 15 plus 15 plus 12 over denominator 2 end fraction = 21
    Area of triangle = square root of 21 left parenthesis 21 minus 15 right parenthesis left parenthesis 21 minus 15 right parenthesis left parenthesis 21 minus 12 right parenthesis end root
    square root of 21 left parenthesis 6 right parenthesis left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end root
    18 square root of 21 cm squared
    So, area of isosceles triangle = 18 square root of 21 cm squared
    NOTE – We can use direct formula of area of isosceles triangle = b over 2 square root of a squared minus b squared over 4 end root where a is an equal side and b is base of triangle
    a = 15 cm , b = 12 cm
    Area of isosceles triangle = 12 over 2 square root of 15 squared minus 12 squared over 4 end root
    square root of 225 minus 144 over 4 end root equals 6 square root of 225 minus 36 end root
    = 6 square root of 189 equals 18 square root of 21 cm squared

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