Calculate the area of an equilateral triangle of side 8cm

1. Analyze the question

You are asked to find the area of an equilateral triangle where each side ($a$) is 8 cm.

2. Explain the concept

An equilateral triangle is a triangle where all three sides are equal in length and all three internal angles are 60°.

The standard formula for the area of an equilateral triangle is derived from the general area formula ($\frac{1}{2} \times \text{base} \times \text{height}$):

Where $a$ is the length of the side of the triangle.

3. Show the solution

• Step 1: Identify the given value. $a = 8 \text{ cm}$
• Step 2: Substitute the value into the formula. $$\text{Area} = \frac{\sqrt{3}}{4} \times (8)^2$$
• Step 3: Calculate the square of the side. $8^2 = 64$
• Step 4: Simplify the expression. $$\text{Area} = \frac{\sqrt{3}}{4} \times 64$$
• Step 5: Divide 64 by 4. $64 \div 4 = 16$
• Step 6: Combine the results. $$\text{Area} = 16\sqrt{3} \text{ cm}^2$$

4. Identify the answer

Comparing our result to the options provided: A. 8√3 B. 16 C. 4√3 D. 16√3

The correct option is D.

5. Tip

To remember this formula easily, think of it as a variation of the standard area formula. Since the height of an equilateral triangle is always $\frac{\sqrt{3}}{2}a$, multiplying this by the base ($a$) and dividing by 2 gives you $\frac{\sqrt{3}}{4}a^2$. Always remember to square the side first before multiplying by the fraction!