Each side of an equilateral triangle measures 8 cm. Find (i) the area of the triangle, correct to 2 places of decimal and (ii) the height of the triangle, correct to 2 places of decimal. (Take `sqrt(3) = 1.732`.)

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the area of the equilateral triangle
The formula for the area \( A \) of an equilateral triangle with side length \( a \) is given by:

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

Given that each side of the triangle measures 8 cm, we substitute \( a = 8 \) cm into the formula.

\[ A = \frac{\sqrt{3}}{4} \times (8)^2 \]

Calculating \( (8)^2 \):

\[ (8)^2 = 64 \]

Now substituting this back into the area formula:

\[ A = \frac{\sqrt{3}}{4} \times 64 \]

Simplifying this:

\[ A = 16\sqrt{3} \]

Now, substituting \( \sqrt{3} \approx 1.732 \):

\[ A = 16 \times 1.732 \]

Calculating this gives:

\[ A \approx 27.712 \]

Rounding to two decimal places, we get:

\[ A \approx 27.71 \, \text{cm}^2 \]

### Step 2: Calculate the height of the equilateral triangle
The formula for the height \( h \) of an equilateral triangle is given by:

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

Substituting \( a = 8 \) cm into the formula:

\[ h = \frac{\sqrt{3}}{2} \times 8 \]

Calculating this:

\[ h = 4\sqrt{3} \]

Now substituting \( \sqrt{3} \approx 1.732 \):

\[ h = 4 \times 1.732 \]

Calculating this gives:

\[ h \approx 6.928 \]

Rounding to two decimal places, we get:

\[ h \approx 6.93 \, \text{cm} \]

### Final Answers:
1. The area of the triangle is approximately \( 27.71 \, \text{cm}^2 \).
2. The height of the triangle is approximately \( 6.93 \, \text{cm} \).

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