Four equilateral triangles of side length 5 cm each

If you have four equilateral triangles with a side length of 5 cm each, there are a few things we can explore, such as calculating the area of one triangle, finding the total area of all four triangles, or even exploring how these triangles can be arranged together.

### 1. Area of One Equilateral Triangle:
The area \( A \) of an equilateral triangle can be calculated using the formula:

\[
A = \frac{\sqrt{3}}{4} \times s^2
\]

where \( s \) is the side length.

Substituting \( s = 5 \) cm:

\[
A = \frac{\sqrt{3}}{4} \times 5^2 = \frac{\sqrt{3}}{4} \times 25 = \frac{25\sqrt{3}}{4} \text{ cm}^2
\]

This is the area of one equilateral triangle.

### 2. Total Area of Four Equilateral Triangles:
If we have four such triangles, the total area \( A_{\text{total}} \) would be:

\[
A_{\text{total}} = 4 \times \frac{25\sqrt{3}}{4} = 25\sqrt{3} \text{ cm}^2
\]

### 3. Arranging the Triangles:
The triangles could be arranged in different ways. If they are arranged to form a larger equilateral triangle, the configuration might alter the total perimeter but not the total area.

Would you like a detailed exploration of how these triangles can be arranged, or do you have a specific question about these triangles?

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Explore how to calculate the area of four equilateral triangles, each with a side length of 5 cm. Understand the formula for the area of an equilateral triangle and compute the total area of these triangles. Suitable for Grades 7-9.

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