Question

Find the area of a triangle whose side measures 13cm,14cm and 12cm

Answer 1

area of a triangle is l×b×h
=13×14×12
=2184

Answer 2

$\bf{\underline{\underline{Answer:}}}$

≈72.30794cm²

$\bf{\underline {Given:}}$

• ABC is a triangle.
• Side a = 13 cm
• Side b = 12 cm
• Side c = 14 cm

$\bf{\underline {To\:Find:}}$

• The semi perimeter (s) of triangle

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Semi perimeter of triangle,

$s = \dfrac{(a+b+c)}{2}\: unit\\ \\</p><p>=\dfrac{(13+12+14)}{2} cm\\ \\</p><p>=\dfrac{39}{2}cm \\ \\= 19.5 cm$

Finding the area of triangle by using the heron's formula :-

$\sf= \sqrt{s(s - a)(s - b)(s - c)}$

Area of triangle

$A=\dfrac{1}{4} \sqrt {-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}$

$=\dfrac{1}{4}\times{\sqrt{-13^4+2 \times(13 \times14)^2+2\times(13 \times12)^2-14^4+2 \times(14 \times12)^2-12^4}}$

≈72.30794cm²