using herons formula
... A is the area ; s is half of the perimeter ; a, b, c are the side lengths
A = √[s(s-a)(s-b)(s-c)]
In triangle ABC,AB=11 cm, BC=9 cm and CA=10 cm. Find the area of the triangle.
2 answers
Semiperemeter:
s = ( a + b + c ) / 2 = ( 11 + 9 + 10 ) / 2 = 30 / 2 = 15 cm
Using Heron's formula,
A = √ [ s ( s - a ) ( s - b ) ( s - c) ]
A = √ [ 15 ( 15 - 11 ) ( 15 - 9 ) ( 15 - 10) ]
A = √ ( 15 ∙ 4 ∙ 6 ∙ 5 )
A = √1800 = √ ( 900 ∙ 2 ) = √900 ∙ √2 = 30 √2 = 42.42641 cm²
s = ( a + b + c ) / 2 = ( 11 + 9 + 10 ) / 2 = 30 / 2 = 15 cm
Using Heron's formula,
A = √ [ s ( s - a ) ( s - b ) ( s - c) ]
A = √ [ 15 ( 15 - 11 ) ( 15 - 9 ) ( 15 - 10) ]
A = √ ( 15 ∙ 4 ∙ 6 ∙ 5 )
A = √1800 = √ ( 900 ∙ 2 ) = √900 ∙ √2 = 30 √2 = 42.42641 cm²