To calculate the area of an equilateral triangle, you need to use the formula designed specifically for equilateral triangles. The formula is given by:
[tex]\[ \text{Area} = \left( \frac{\sqrt{3}}{4} \right) \times (\text{side length})^2 \][/tex]
For an equilateral triangle with a side length of 10 cm, you can follow these steps:
1. Side Length:
The side length ([tex]\(a\)[/tex]) of the equilateral triangle is given as 10 cm.
2. Square the Side Length:
Calculate the square of the side length:
[tex]\[ a^2 = 10^2 = 100 \][/tex]
3. Constant Multiplication:
The constant factor involving the square root of 3 over 4 is:
[tex]\[ \frac{\sqrt{3}}{4} \][/tex]
4. Combine the Values:
Multiply the constant factor by the square of the side length to find the area of the triangle:
[tex]\[ \text{Area} = \left( \frac{\sqrt{3}}{4} \right) \times 100 \][/tex]
5. Final Calculation:
Perform the multiplication to get the final numerical value of the area:
[tex]\[ \text{Area} = 43.30127018922193 \, \text{cm}^2 \][/tex]
Therefore, the area of an equilateral triangle with sides of 10 cm is approximately [tex]\( 43.30127018922193 \, \text{cm}^2 \)[/tex].
