At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine the area of an equilateral triangle with a given perimeter of 24 inches, we'll follow these steps:
1. Determine the side length of the equilateral triangle:
- Since the perimeter of an equilateral triangle is the sum of the lengths of all three equal sides, we can find the side length by dividing the perimeter by 3.
[tex]\[ \text{Side length} = \frac{\text{Perimeter}}{3} = \frac{24}{3} = 8 \text{ inches} \][/tex]
2. Use the side length to find the area:
- The formula for the area of an equilateral triangle is given by:
[tex]\[ \text{Area} = \frac{\sqrt{3}}{4} \times \text{side length}^2 \][/tex]
- Plugging in the side length we determined earlier:
[tex]\[ \text{Area} = \frac{\sqrt{3}}{4} \times 8^2 \][/tex]
- First, calculate \(8^2\):
[tex]\[ 8^2 = 64 \][/tex]
- Then multiply by \(\frac{\sqrt{3}}{4}\):
[tex]\[ \text{Area} = \frac{\sqrt{3}}{4} \times 64 \approx 27.712812921102035 \text{ square inches} \][/tex]
3. Round the area to the nearest tenth:
- The area calculated above is approximately \(27.712812921102035\) square inches.
- Rounding to the nearest tenth:
[tex]\[ 27.712812921102035 \approx 27.7 \text{ square inches} \][/tex]
Thus, the area of the equilateral triangle, rounded to the nearest tenth of square inch, is:
[tex]\[ \text{Area} = 27.7 \text{ square inches} \][/tex]
1. Determine the side length of the equilateral triangle:
- Since the perimeter of an equilateral triangle is the sum of the lengths of all three equal sides, we can find the side length by dividing the perimeter by 3.
[tex]\[ \text{Side length} = \frac{\text{Perimeter}}{3} = \frac{24}{3} = 8 \text{ inches} \][/tex]
2. Use the side length to find the area:
- The formula for the area of an equilateral triangle is given by:
[tex]\[ \text{Area} = \frac{\sqrt{3}}{4} \times \text{side length}^2 \][/tex]
- Plugging in the side length we determined earlier:
[tex]\[ \text{Area} = \frac{\sqrt{3}}{4} \times 8^2 \][/tex]
- First, calculate \(8^2\):
[tex]\[ 8^2 = 64 \][/tex]
- Then multiply by \(\frac{\sqrt{3}}{4}\):
[tex]\[ \text{Area} = \frac{\sqrt{3}}{4} \times 64 \approx 27.712812921102035 \text{ square inches} \][/tex]
3. Round the area to the nearest tenth:
- The area calculated above is approximately \(27.712812921102035\) square inches.
- Rounding to the nearest tenth:
[tex]\[ 27.712812921102035 \approx 27.7 \text{ square inches} \][/tex]
Thus, the area of the equilateral triangle, rounded to the nearest tenth of square inch, is:
[tex]\[ \text{Area} = 27.7 \text{ square inches} \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.