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Question
Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm
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Solution
Let a = 10 cm, b = 24 cm and c = 26 cm
s = `("a" + "b" + "c")/2`
= `(10 + 24 + 26)/2`
s = `60/2`
= 30 cm
s – a = 30 – 10 = 20 cm
s – b = 30 – 24 = 6 cm
s – c = 30 – 26 = 4 cm
Area of a triangle
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`
= `sqrt(30 xx 20 xx 6 xx 4)`
= `sqrt(2 xx 3 xx 5 xx 2^2 xx 5 xx 2 xx 3 xx 2^2)`
= `sqrt(2^6 xx 3^2 xx 5^2)`
= 23 × 3 × 5
= 8 × 3 × 5
= 120 cm2
Area of a triangle = 120 cm2
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