find the area of a triangle whose sides are 10cm, 12cm,14cm
Answers
Answer:
Area of triangle =24√6cm square
Step-by-step explanation:
s=a+b+c/2=10+12+14 /2 =36/2=18cm
s=18cm
Area of triangle =√s(s-a)(s-b)(s-c)
=√18(18-10)(18-12)(18-14)
=√18(8)(6)(4)
=√18×8×6×4
=√3×3×2×2×2×2×2×3×2×2
=3×2×2×2√2×3
=24√6cm square
Step-by-step explanation:
The area of a triangle when the lengths of the three sides a, b, c are known is given by the Heron’s formula viz.,
Sq rt {s(s-a)(s-b)(s-c)} where s is the semi-perimeter of the triangle ………(1)
Now s = (a+b+c)/2 = (12+14+10)/2 = 18, s-a = 18–12 = 6, s-b = 18–14 =4 and s-c= 18–10 =8
Substituting theses values in (1) we have, sq rt {18(6)(4)(8) = 24 (rt 6) = 58.79 (approx)
Therefore, the area of the required triangle is 58.79 sq.cm (approx.)
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