Question

find the area of isosceles triangle with perimeter 36 cm and base is 6 cm

Answer 1

let each equal side be x cm.

$\textbf{\underline{Perimeter of a triangle}}$ $\underline{\textbf{ = sum of all three sides }}$

Since, two sides are equal , then three sides become

x, x and 6 cm.

36 = x+x+6

36=2x+6

36-6=2x

30=2x

$\bf{ \frac{30}{2} = x}$

15=x

$\bf{\underline{semiperimeter \: (s) = \frac{perimeter}{2}}}$

$= \frac{36}{2}$

$= 18 \: cm$

$\underline {\bf{area \: of \: triangle \: by \: herons \: formula \: -} }$

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

$= \sqrt{18(18 - 15)(18 - 15)(18 - 6)}$

$= \sqrt{18(3)(3)(12)}$

$= \sqrt{3 \times 3 \times 2 \times 3 \times 3 \times 3 \times 2 \times 2}$

$= 3 \times 3 \times 2 \sqrt{3 \times 2}$

$= 18 \sqrt{6 \: }{cm {}^{2} }$