Question

The sides of the triangles are 7,6,8. so find the area of the triangles. find area

Answer 1

ɢɪᴠᴇɴ :-

• Sides of Triangle are 7cm , 6cm , 8cm

Tᴏ Fɪɴᴅ :-

• Area of Triangle

Sᴏʟᴜᴛɪᴏɴ :-

We know that,

➠ Area of Triangle. = √s(s-a) (s-b) (s-c)

where,

➠ s = Perimeter of Triangle / 2

➠ s = (a + b + c) / 2

➠ s = ( 8+ 7+ 6) / 2

➠ s = 21/2 = 10.5cm

➠ a , b, c are sides of Triangle

Now,

$\tt Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \implies\tt \: \sqrt{10.5(10.5 - 7)(10 .5 - 6)(10.5 - 8)} \\ \\ \implies\tt \: \sqrt{10.5 \times 3.5 \times 4.5 \times 2.5} \\ \\ \implies\tt \: \sqrt{413.4375} = 20.33 {cm}^{2}$

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Mᴏʀᴇ Fᴏʀᴍᴜʟᴀs :-

• Area of Triangle = 1/2 × base × height

• Area of Equilateral triangle = √3a²/4

• Area of Isosceles Triangle = b/4 . √(4a² - b²)

• Perimeter of Equilateral triangle = 3a

Answer 2

${\bf{\underline{\underline{\bigstar\: Figure : }}}}$

$\:\:$

$\setlength{\unitlength}{1.6mm}\begin{picture}(50,20)\linethickness{0.1mm}\put(-3,-3){\line(1,1){20}}\put(36.6,-2.8){\line(-1,1){19.8}}\put(-3,-3){\line(1,0){39.5}}\put(30,6){6}\put(3,6){7}\put(15,-5){8}\end{picture}$

$\:\:$

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

$\:\:$

• $\red{\footnotesize{ First\: side(a) = 7 }}$

• $\red{\footnotesize{ Second\: side(b) = 6 }}$

• $\red{\footnotesize{ Third\: side(c) = 8 }}$

$\:\:$

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

$\:\:$

• $\red{\footnotesize{ Area\:of\: triangle }}$

$\:\:$

${\bf{\underline{\underline{\bigstar\: Solution : }}}}$

$\:\:$

$\orange{\footnotesize{ Semi\: perimeter(s) = \dfrac{7 + 6 + 8}{2} }}$

$\orange{\footnotesize{\implies Semi\: perimeter(s) = \dfrac{21}{2} }}$

$\orange{\footnotesize{\implies Semi\: perimeter(s) = 10.5 }}$

$\:\:$

$\rule{200}2$

$\:\:$

$\blue{\footnotesize{ Area\:of\: triangle = \sqrt{ S ( s - a)(s - b)(s - c)}}}$

$\blue{\footnotesize{\implies Area\:of\: triangle = \sqrt{ 10.5 ( 10.5 - 7)(10.5 - 6)(10.5 - 8)}}}$

$\blue{\footnotesize{\implies Area\:of\: triangle = \sqrt{ 10.5 \times 3.5 \times 4.5 \times 2.5}}}$

$\blue{\footnotesize{\implies Area\:of\: triangle = \sqrt{413.43}}}$

$\blue{\footnotesize{\implies Area\:of\: triangle = 20.33}}$