If the sides of a triangle are $$ 50.5 \mathrm{~cm}, 70 \mathrm{~cm} $$, and 62.7 cm long, then the area of the triangle is $$ \square $$. Your answer will be numerical only).

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To find the area of a triangle when all three sides are known, we can use Heron's formula.

Heron's formula states that the area of a triangle with sides of length $$ a $$, $$ b $$, and $$ c $$ is given by:

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

where $$ s $$ is the semi-perimeter of the triangle, calculated as:

$$ s = \frac{a + b + c}{2} $$

Given the sides of the triangle are $$ 50.5 \mathrm{~cm}, 70 \mathrm{~cm} $$, and $$ 62.7 \mathrm{~cm} $$, we can calculate the semi-perimeter and then use Heron's formula to find the area of the triangle.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(50.5+70+62.7\right)}{2}$$
- step1: Remove the parentheses:
  $$\frac{50.5+70+62.7}{2}$$
- step2: Add the numbers:
  $$\frac{183.2}{2}$$
- step3: Convert the expressions:
  $$\frac{\frac{916}{5}}{2}$$
- step4: Multiply by the reciprocal:
  $$\frac{916}{5}\times \frac{1}{2}$$
- step5: Reduce the numbers:
  $$\frac{458}{5}\times 1$$
- step6: Multiply:
  $$\frac{458}{5}$$
The semi-perimeter of the triangle is $$ 91.6 $$ cm.

Now, we can use Heron's formula to find the area of the triangle:

$$ \text{Area} = \sqrt{91.6(91.6-50.5)(91.6-70)(91.6-62.7)} $$

Let's calculate the area of the triangle.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{91.6\left(91.6-50.5\right)\left(91.6-70\right)\left(91.6-62.7\right)}$$
- step1: Subtract the numbers:
  $$\sqrt{91.6\times 41.1\left(91.6-70\right)\left(91.6-62.7\right)}$$
- step2: Subtract the numbers:
  $$\sqrt{91.6\times 41.1\times 21.6\left(91.6-62.7\right)}$$
- step3: Subtract the numbers:
  $$\sqrt{91.6\times 41.1\times 21.6\times 28.9}$$
- step4: Multiply the terms:
  $$\sqrt{2350113.7824}$$
- step5: Rewrite the expression:
  $$\sqrt{\frac{1468821114}{625}}$$
- step6: Use the properties of radicals:
  $$\frac{\sqrt{1468821114}}{\sqrt{625}}$$
- step7: Simplify the expression:
  $$\frac{153\sqrt{62746}}{25}$$
The area of the triangle is approximately $$ 1533.008083 $$ square centimeters.
The area of the triangle is approximately $$ 1533.01 $$ cm².

If the sides of a triangle are , and 62.7 cm long, then the area of the triangle is . Your
answer will be numerical only).

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If the sides of a triangle are , and 62.7 cm long, then the area of the triangle is . Your answer will be numerical only).