The perimeter of an equilateral triangle is 90 cm. Find its area.

Options

A. 225V3 sq cm
B. 250V3 sq cm
C. 135V3 sq cm
D. 151V3 sq cm

Answer

To find the area of an equilateral triangle given its perimeter, we can follow these steps:

### Step 1: Understand the properties of an equilateral triangle
An equilateral triangle has all three sides equal in length. The perimeter (P) of an equilateral triangle can be expressed as:
\[ P = 3 \times \text{side length} \]

### Step 2: Set up the equation using the given perimeter
We are given that the perimeter of the triangle is 90 cm. Therefore, we can set up the equation:
\[ 90 = 3 \times \text{side length} \]

### Step 3: Solve for the side length
To find the side length, we need to divide the perimeter by 3:
\[ \text{side length} = \frac{90}{3} = 30 \text{ cm} \]

### Step 4: Use the formula for the area of an equilateral triangle
The area (A) of an equilateral triangle can be calculated using the formula:
\[ A = \frac{\sqrt{3}}{4} \times \text{side length}^2 \]

### Step 5: Substitute the side length into the area formula
Now, substituting the side length we found:
\[ A = \frac{\sqrt{3}}{4} \times (30)^2 \]

### Step 6: Calculate the area
First, calculate \( (30)^2 \):
\[ (30)^2 = 900 \]
Now substitute this value into the area formula:
\[ A = \frac{\sqrt{3}}{4} \times 900 \]

### Step 7: Simplify the expression
Now simplify:
\[ A = 225\sqrt{3} \text{ cm}^2 \]

### Final Answer
Thus, the area of the equilateral triangle is:
\[ A = 225\sqrt{3} \text{ cm}^2 \]

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