**Finding the Area of an Equilateral Triangle**

To find the area of an equilateral triangle, we can use the formula:

Area = (side^2 * √3) / 4

Given that the length of each side is 24 cm, we can substitute this value into the formula to find the area.

**Substituting the Values**

Area = (24^2 * √3) / 4

Simplifying the equation:

Area = (576 * 1.73) / 4

Area = 995.04 / 4

Area ≈ 248.76 cm^2

**Explanation:**

- The area of any triangle can be calculated using the formula: Area = (base * height) / 2. However, for an equilateral triangle, the height can be determined by drawing a perpendicular line from one corner to the midpoint of the opposite side, creating two right-angled triangles.
- In an equilateral triangle, all three sides are equal, so if we draw a perpendicular line from one corner to the midpoint of the opposite side, it will bisect the side into two equal parts.
- This perpendicular line is also the height of the equilateral triangle. It divides the equilateral triangle into two right-angled triangles, each with a base equal to half the length of one side and a height equal to the height of the equilateral triangle.
- Since the triangle is equilateral, the two right-angled triangles formed are congruent, meaning they have the same dimensions.
- By using the Pythagorean theorem, we can determine the height of the equilateral triangle. Let's denote the side length as 's' and the height as 'h'. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- In our equilateral triangle, the hypotenuse is the side 's', and the other two sides are 'h' and 's/2'. Applying the Pythagorean theorem, we get: s^2 = h^2 + (s/2)^2.
- Since the triangle is equilateral, all sides are equal, so we can substitute 's' for 24 cm.
- Solving the equation, we find: 24^2 = h^2 + (24/2)^2.
- Simplifying further: 576 = h^2 + 144.
- Rearranging the equation: h^2 = 576 - 144 = 432.
- Taking the square root of both sides, we find: h = √432 = 20.7846 cm.
- Now that we have the height, we can calculate the area of the equilateral triangle using the formula: Area = (base * height) / 2. The base is equal to the side length, which is 24 cm.
- Substituting the values into the formula, we get: Area = (24 * 20.7846) / 2 = 497.2304 / 2 = 248.76 cm^2 (rounded to two decimal places).
- Therefore, the area of an equilateral triangle with sides measuring 24 cm each is approximately 248.76 cm^2.

Area of equilateral triangle=√3/4×a^2
=√3/4×(24^2)

=√3/4×24×24
=√3×144

=1.73×144


=249.12 cm^2(Ans).

please ; upvote my answer |;