https://file.aiquickdraw.com/mathbot/file/1725812311952s3q2vez5.jpg

A)what is the length of its sideB)area of this triangle

This image shows an equilateral triangle, with a vertical altitude drawn from the top vertex to the midpoint of the base. The altitude creates two right triangles, and the image also indicates that the height (altitude) is \( \sqrt{3} \).

### A) Finding the side length of the equilateral triangle:
For an equilateral triangle, the relationship between the height \( h \) and the side length \( s \) is:

\[
h = \frac{\sqrt{3}}{2} s
\]

Given that \( h = \sqrt{3} \), we substitute and solve for \( s \):

\[
\sqrt{3} = \frac{\sqrt{3}}{2} s
\]

Multiply both sides by 2:

\[
2 \cdot \sqrt{3} = \sqrt{3} \cdot s
\]

Now divide by \( \sqrt{3} \) to isolate \( s \):

\[
s = 2
\]

So, the side length \( s \) is 2 units.

### B) Finding the area of the equilateral triangle:
The area \( A \) of an equilateral triangle can be calculated using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

The base is equal to the side length, which we found to be 2 units, and the height is given as \( \sqrt{3} \). Substituting these values:

\[
A = \frac{1}{2} \times 2 \times \sqrt{3} = \sqrt{3} \, \text{square units}
\]

Thus, the area of the triangle is \( \sqrt{3} \) square units.

Would you like further details or clarification on any steps?

Here are some related questions for practice:
1. What is the perimeter of this equilateral triangle?
2. How does the area formula for an equilateral triangle relate to its side length directly?
3. What is the ratio of the height to the base in an equilateral triangle?
4. How does the altitude divide an equilateral triangle into two 30-60-90 triangles?
5. What is the relationship between the circumradius and the side length of an equilateral triangle?

**Tip:** For any equilateral triangle, you can always use the relationship \( h = \frac{\sqrt{3}}{2} s \) to quickly find the side length if the height is known.

A) What is the length of its side? B) What is the area of this triangle?

Learn how to find the side length and area of an equilateral triangle given its height of √3 units. This problem involves using the formulas for the height and area of an equilateral triangle, and understanding properties of right triangles. Suitable for students in Grades 9-10.

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