Question

$\underline{\Huge{\purple{\sf Question:-}}}$


A triangular field has sides measure 5cm ,12cm,13cm.

Find the perimeter and area of the field.

Note:-

Answer must be in 45+words

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Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• A triangular field has sides measure measure 5 cm, 12 cm, 13 cm.  Find the Perimeter and Area of the Field

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Length of Triangular Field Sides : 5 cm, 12 cm, 13 cm

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Perimeter of the Field  with Given Measures of Sides

• Area of the Field with Given Measures of Sides

$\underline{\underline{\sf{\maltese\:\:Formulas\:Used}}}$

• Perimeter of Triangle = Sum of All Sides

• Area of Triangle = $\sf{\sqrt{\mathsf{s}(\mathsf{s}-\mathsf{a})(\mathsf{s}-\mathsf{b})(\mathsf{s}-\mathsf{c})}}$

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Perimeter of Triangle Field = 30 cm

• Area of Triangle Field = 30 cm²

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

We know Perimeter of Triangle = Sum of All Sides

⇒ Perimeter of Triangle = 5 cm + 12 cm + 13 cm

⇒ Perimeter of Triangle = 5 + 12 + 13 cm

⇒ Perimeter of Triangle = 30 cm

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf 5\ cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 13\ cm }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf 12\ cm }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C } \put(1.2, - 2.3){ \large\boxed{\bigstar\:{\mathfrak{\sf{P}\mathfrak{erimeter\:=\:30\:cm}}}} } \put(1.2, 4.5){ \sf \underline{\underline{@RockingStarPratheek}} } \end{picture}$

Now, We shall calculate Semi Perimeter to Find out the Area of Triangle and To Find Semi Perimeter, We need to use this formula :

$\bigstar\:\:\sf{Semi perimeter=\dfrac{a+b+c}{2}}$

• Where a, b, c  are sides of the Triangle

$\longrightarrow\:\:\sf{Semi perimeter=\dfrac{a+b+c}{2}}$

$\longrightarrow\:\:\sf{Semi perimeter=\dfrac{5\:cm + 12\: cm + 13 \:cm}{2}}$

$\longrightarrow\:\:\sf{Semi perimeter=\dfrac{30 \:cm}{2}}$

$\boxed{\bigstar\to\:\:\sf{Semi perimeter=15\:cm}}$

Or We can Simplify Find Semi perimeter by Dividing Perimeter by 2

$\longrightarrow\:\:\sf{Semi perimeter=\dfrac{Perimeter}{2}}$

$\longrightarrow\:\:\sf{Semi perimeter=\dfrac{30\:cm}{2}}$

$\boxed{\bigstar\to\:\:\sf{Semi perimeter=15\:cm}}$

We Also Know Area of Triangle = $\sf{\sqrt{\mathsf{s}(\mathsf{s}-\mathsf{a})(\mathsf{s}-\mathsf{b})(\mathsf{s}-\mathsf{c})}}$  (Herons Formula)

Substitute the values of Semi perimeter - s, Sides of Triangular Field - a, b, c

⇒ Area of Triangle = $\sf{\sqrt{\mathsf{15}(\mathsf{15}-\mathsf{5})(\mathsf{15}-\mathsf{12})(\mathsf{15}-\mathsf{13})}}$

⇒ Area of Triangle = $\sf{\sqrt{\mathsf{15}(10)(3)(2)}}$

⇒ Area of Triangle = $\sf{\sqrt{\mathsf{15\times 10\times 3\times 2}}}$

⇒ Area of Triangle = $\sf{\sqrt{\mathsf{900}}}$

⇒ Area of Triangle = $\sf{\mathsf{30\:cm^2}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf 5\ cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 13\ cm }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf 12\ cm }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C } \put(1.2, - 2.3){ \large\boxed{\bigstar\:{\mathfrak{\sf{A}\mathfrak{rea\:=\:30\:cm^2}}}} } \put(1.2, 4.5){ \sf \underline{\underline{@RockingStarPratheek}} } \end{picture}$

$\underline{\underline{\sf{\maltese\:\:Request}}}$

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Answer 2

$\huge\red{\mid{\underline{\overline{\texttt{Question}}}\mid}}$

A triangular field has sides measure 5cm 12cm,13cm. Find the perimeter and area of the field.

$\huge \pink{\mid{\fbox{\tt{Answer}}\mid}}$

PERIMETER = 30cm²

AREA = 30cm

$\huge\purple{\mid{\fbox{\tt{Solution}}\mid}}$

$\tt \red {GIVEN : }$

TRIANGLE OF SIDES = 5cm, 12cm and 13 cm

$_____________________________________________$

$\tt \orange {LET \: BE : }$

Let be the sides of triangle be a,b and c respectively

Therefore,

a = 5cm

b = 12cm

c = 13cm

$_____________________________________________$

$\tt \blue {TO \: FIND :}$

PERIMETER OF TRIANGLE = ?

AREA OF TRIANGLE = ?

$_____________________________________________$

$\tt \green {FORMULA \: USED : }$

AREA OF TRIANGLE =

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

where,

s is semiperimeter of the triangle (for finding semiperimeter of a triangle,the perimeter is halved ,so,

semiperimeter = perimeter/2)

a, b and c are sides of triangle.

__________________________________

PERIMETER OF TRIANGLE =

a + b + c ------- (sum of all sides of triangle)

where,

a,b and c are sides of triangle

$_____________________________________________$

$\tt \purple {CALCULATIONS : }$

PERIMETER OF TRIANGLE = a + b + c

PERIMETER OF TRIANGLE = 5 + 12 + 13

PERIMETER OF TRIANGLE = 30cm

Therefore,

SEMIPERIMETER = PERIMETER/2 = 30/2 = 15cm

AREA OF TRIANGLE =

$\tt\implies\sqrt{s(s - a)(s - b)(s - c)}$

$\tt \implies \sqrt{15(15 - 5)(15- 12)(15 - 13}$

$\tt \implies \: \sqrt{15(10)(3)(2)}$

$\tt\implies \: \sqrt{900}$

$\tt\implies \: \sqrt{30c {m}^{2} }$

HENCE ,

AREA OF TRIANGLE IS 30cm²

PERIMETER OF TRIANGLE is 30cm