Question

Plz do it fast

I will mark as brainlist​

Answer 1

Answer:

180/3=length of each side

60= length of each side

semi perimeter= 180/2= 90

herons formula

under root (90(90-60)(90-60)(90-60))

ans = 900 UNDER ROOT 3

Answer 2

Question:

${\tt{ \bold {\green{A \: traffic \: signal \: board \: indicating \: "School \: Ahead" \: is \: an \: equilateral \: triangle \: with \: side \: 'a'.Find \: the}}}} \\ { \tt{ \green{ \bold{board \: using \: heron's \: formula,if \: the \: perimeter \: is \: 180 \: cm. What \: will \: be \: the \: area \: of \: signal \: board?}}}}$

Answer:

900√3 cm^2

Explanation:

$\bold {Area \: of \: the \: triangle \: by \: heron's \: formula} \\ \: \: \: \: \: \: \: \: \: \: \: \large{ \green{ \tt { \sqrt{s(s - a)(s - b)(s - c)} }}}$

$\tt \: Given \: that \: it \: is \: an \: equilateral \: triangle, \\ \tt \: So, all \: the \: sides \: will \: be \: equal. \\ \tt \: ∴a=b=c \\ \\ \tt \: Semi perimeter=S= \red{\frac{ Perimeter}{2}} \\ \tt \: Semi perimeter=S= \frac{a + b + c}{2} \\ \tt \: Semi perimeter=S= \frac{3a}{2} \\ \\ \tt \: = \large{ { \tt { \sqrt{s(s - a)(s - b)(s - c)} }}} \\ \tt \: putting \: a = b = c = \frac{3a}{2}$

$\tt \bold {Area \: of \: Signal \: board:} \\ \tt \: = \sqrt{ \frac{3a}{2}{\huge{(}}\frac{3a}{2} - a{\huge{)}}{\huge{(}} \frac{3a}{2} - a{\huge{)}} {\huge{(}} \frac{3a}{2} - a{\huge{)}}} \\ \\ = \tt \: \sqrt{ \frac{3a}{2} \times \frac{a}{2}\times \frac{a}{2}\times \frac{a}{2} } \\ \\ \tt \: = \sqrt{ \frac{3 {a}^{4} }{ {2}^{4} } } \\ \\ \tt \: = \frac{ \sqrt{3 {a}^{2} } }{ {2}^{2} } ⇢ i) \\ \\ \tt \: = \frac{ \sqrt{3 {a}^{2} } }{4}$

$\tt \: If \: perimeter \: is \: 180 \: cm. \\ \tt \: a + a + a = 180\\ \tt \: 3a = 180\\ \tt \: a = \frac{180}{3} \\ \tt \bold {a= 60 \: cm} \\ \\ \tt \: Putting \: a=60 \: cm \: in \: eq. I) \\ \tt \bold{Area \: of \: traingle} = \frac{ \sqrt{3 {a}^{2} } }{4} \\ \tt \: \bold{Area \: of \: traingle} = \frac{ \sqrt{3}(60) {}^{2} }{4} \\ \bold{Area \: of \: traingle} = \frac{ \sqrt{3} \times 3600}{4} \\ \bold{Area \: of \: traingle} = 900 \sqrt{3} {cm}^{2}$

$\huge \bold {{@QianNiu}}$