Question

answer me in copy please ​

Answer 1

Given :-

• Perimeter of equilateral triangle =162cm

To Find :-

• We have to find the Area of equilateral triangle using herons Formula

Now find the sides of triangle

• In equilateral triangle all sides are equal

• Let the side be a

$\underline{\bigstar{\sf Perimeter\ of \ triangle = Sum \ of \ all \ sides }}$

$\dashrightarrow\sf a+a+a=162\\ \\ \dashrightarrow\sf 3a=162\\ \\\dashrightarrow\sf a =\cancel{\dfrac{162}{3}}\\ \\\dashrightarrow\sf a=54$

$\boxed{\sf Side\ of \ triangle = 54 \ cm }$

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

• Where a ,b and c are the sides of triangle
• And s = semi perimeter

★ Now find the semi Perimeter

$\dashrightarrow\sf s=\dfrac{a+b+c}{2}\\ \\\dashrightarrow\sf s=\dfrac{54+54+54}{2}\\ \\\dashrightarrow\sf s= \cancel{\dfrac{162}{2}}\\ \\\dashrightarrow{\red{\sf semi \ perimeter= 81cm}}$

• Now find the Area of triangle using the herons Formula

$\dashrightarrow\sf Area \ of \ \triangle = \sqrt{s(s-a)(s-b)(s-c)}\\ \\\dashrightarrow\sf Area =\sqrt{81(81-54)(81-54)(81-54)}\\ \\\dashrightarrow\sf Area = \sqrt{81\times 27\times 27\times 27}\\ \\\dashrightarrow\sf Area = \sqrt{27\times 3\times 27\times 27\times 27}\\ \\\dashrightarrow\sf Area = 27\times 27\sqrt{3}\\ \\\dashrightarrow\sf Area = 729\times 1.73 \ \ \ \ \ \ \therefore\Big[ \sqrt{3}=1.73\Big]\\ \\\dashrightarrow{\blue{\sf Area = 1261.17cm^2}}$

$\underline{\boxed{\sf Area \ of \ triangle =1261.17cm^2}}$

Answer 2

Solution

Given Here :-

• Perimeter of equilateral triangle = 162 cm

Find :-

• Area of equilateral triangle , by using Heron's Formula

Explanation

We know,

Equilateral triangle have all equal side

So, we can take here x be the side of this triangle .

Using Formula

★ Perimeter of equilateral triangle = Sum of all equal side

==> x + x + x = 162

==> 3x = 162

==> x = 162/3

==> x = 54

Since

Equal side of equilateral triangle be = 54 cm

Now, Calculate Area by Heron's Formula

For this take a ∆ABC here,

Where,

• AB = 54 cm
• BC = 54 cm
• CA = 54 cm

Now, Using Formula

★ Semi - perimeter(S) = (AB+BC+CA)/2

Keep above values,

==> Semi - perimeter(S) = (54+54+54)/2

==> Semi - perimeter(S) = 81 cm

By, Heron's Formula

★Area = √[S(S-AB)(S-BC)(S-CA)]

Keep all above values

==> Area = √[81(81-54)(81-54)(81-54)]

==> Area = √[81* 27 * 27 * 27]

==> Area = √(9×9×27×27×3×3×3)

==> Area = 9×27×3 × √3

==> Area = 729× 1.732 [ √3 = 1.73 ]

==> Area = 1261. 16cm²

Hence,

• Area of equilateral triangle will be = 1261.16cm²

_________________