What Is The Area Of An Equilateral Triangle That Has A Perimeter Of 36 Centimeters? Round To The Nearest Square Centimeter.A. 15 Square Centimeters B. 25 Square Centimeters C. 62 Square Centimeters D. 72 Square Centimeters Perimeter $= 36 \,

Understanding the Basics of an Equilateral Triangle

An equilateral triangle is a type of triangle where all three sides are equal in length. This unique property makes it easier to calculate various properties of the triangle, such as its area. In this article, we will explore how to find the area of an equilateral triangle with a given perimeter.

Calculating the Side Length of the Equilateral Triangle

To find the area of the equilateral triangle, we first need to calculate the length of its sides. Since the perimeter of the triangle is given as 36 centimeters, we can use the formula for the perimeter of an equilateral triangle, which is:

Perimeter = 3 × side length

We can rearrange this formula to solve for the side length:

Side length = Perimeter ÷ 3

Substituting the given perimeter value, we get:

Side length = 36 ÷ 3 Side length = 12 centimeters

Calculating the Area of the Equilateral Triangle

Now that we have the side length of the equilateral triangle, we can use the formula for the area of an equilateral triangle, which is:

Area = (√3 ÷ 4) × side length^2

Substituting the side length value, we get:

Area = (√3 ÷ 4) × 12^2 Area = (√3 ÷ 4) × 144 Area = 0.433 × 144 Area = 62.112 square centimeters

Rounding to the nearest square centimeter, we get:

Area ≈ 62 square centimeters

Conclusion

In this article, we have explored how to find the area of an equilateral triangle with a given perimeter. We first calculated the side length of the triangle using the formula for the perimeter of an equilateral triangle. Then, we used the formula for the area of an equilateral triangle to find the area. The final answer is approximately 62 square centimeters.

Frequently Asked Questions

Q: What is the formula for the perimeter of an equilateral triangle?

A: The formula for the perimeter of an equilateral triangle is Perimeter = 3 × side length.

Q: What is the formula for the area of an equilateral triangle?

A: The formula for the area of an equilateral triangle is Area = (√3 ÷ 4) × side length^2.

Q: How do I round the area to the nearest square centimeter?

A: To round the area to the nearest square centimeter, you can use a calculator or round the value manually.

Step-by-Step Solution

Step 1: Calculate the side length of the equilateral triangle

Side length = Perimeter ÷ 3 Side length = 36 ÷ 3 Side length = 12 centimeters

Step 2: Calculate the area of the equilateral triangle

Area = (√3 ÷ 4) × side length^2 Area = (√3 ÷ 4) × 12^2 Area = (√3 ÷ 4) × 144 Area = 0.433 × 144 Area = 62.112 square centimeters

Step 3: Round the area to the nearest square centimeter

Area ≈ 62 square centimeters

Final Answer

The final answer is: $\boxed{62}$

Understanding Equilateral Triangles

An equilateral triangle is a type of triangle where all three sides are equal in length. This unique property makes it easier to calculate various properties of the triangle, such as its area and perimeter. In this article, we will explore some frequently asked questions about equilateral triangles.

Q&A: Equilateral Triangle Properties

Q: What is the formula for the perimeter of an equilateral triangle?

A: The formula for the perimeter of an equilateral triangle is Perimeter = 3 × side length.

Q: What is the formula for the area of an equilateral triangle?

A: The formula for the area of an equilateral triangle is Area = (√3 ÷ 4) × side length^2.

Q: How do I calculate the side length of an equilateral triangle if I know its perimeter?

A: To calculate the side length of an equilateral triangle, you can use the formula: Side length = Perimeter ÷ 3.

Q: How do I calculate the area of an equilateral triangle if I know its side length?

A: To calculate the area of an equilateral triangle, you can use the formula: Area = (√3 ÷ 4) × side length^2.

Q: What is the relationship between the side length and the area of an equilateral triangle?

A: The area of an equilateral triangle is directly proportional to the square of its side length.

Q: Can I use the same formula to calculate the area of a scalene triangle?

A: No, the formula for the area of an equilateral triangle is specific to equilateral triangles and cannot be used for scalene triangles.

Q: How do I round the area of an equilateral triangle to the nearest square centimeter?

A: To round the area of an equilateral triangle to the nearest square centimeter, you can use a calculator or round the value manually.

Q&A: Equilateral Triangle Examples

Q: What is the area of an equilateral triangle with a side length of 10 centimeters?

A: To calculate the area of an equilateral triangle with a side length of 10 centimeters, you can use the formula: Area = (√3 ÷ 4) × side length^2. Substituting the side length value, you get: Area = (√3 ÷ 4) × 10^2 = 43.3 square centimeters.

Q: What is the perimeter of an equilateral triangle with an area of 50 square centimeters?

A: To calculate the perimeter of an equilateral triangle with an area of 50 square centimeters, you can use the formula: Perimeter = 3 × side length. First, you need to find the side length of the triangle using the formula: side length = √(4 × area ÷ √3). Substituting the area value, you get: side length = √(4 × 50 ÷ √3) = 7.66 centimeters. Then, you can calculate the perimeter: Perimeter = 3 × 7.66 = 22.98 centimeters.

Q&A: Equilateral Triangle Formulas

Q: What is the formula for the height of an equilateral triangle?

A: The formula for the height of an equilateral triangle is Height = (√3 ÷ 2) × side length.

Q: What is the formula for the median of an equilateral triangle?

A: The formula for the median of an equilateral triangle is Median = side length.

Q: What is the formula for the altitude of an equilateral triangle?

A: The formula for the altitude of an equilateral triangle is Altitude = (√3 ÷ 2) × side length.

Conclusion

In this article, we have explored some frequently asked questions about equilateral triangles. We have covered topics such as the formula for the perimeter and area of an equilateral triangle, how to calculate the side length and area of an equilateral triangle, and the relationship between the side length and area of an equilateral triangle. We have also provided examples and formulas for calculating the height, median, and altitude of an equilateral triangle.