Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
9-inch perimeter
A = sq. in.
Each side = 3 inches
By drawing a line from the center of the base to the top vertex you'll divide the triangle into two triangles.
The base = 1.5"
a^2 + b^2 = c^2
a^2 + 1.5^2 = 3^2
a^2 + 2.25 = 9
a^2 = 6.75
a = 2.6
A = 1/2bh
A = (1/2) * 1.5 * 2.6
A = ?
A=(1/2)*(base)*(height)
Side length=(1/3)*(9)=3
Split the triangle in half. This will give you the base, 1.5 in.
If you can image, you have two hypotenuse triangles. To find the height, you need to find the length of the line used to split the triangle in half. So, using Pythagorean Theorem, A^2 + B^2 = C^2 or (1.5)^2 + B^2 = (3)^2.
To find the area of an equilateral triangle, we need to use the formula:
A = (s^2 * √3) / 4
where A is the area and s is the side length of the triangle.
Given that the perimeter of the equilateral triangle is 9 inches, we can find the length of each side by dividing the perimeter by 3:
s = 9 inches / 3 = 3 inches
Now that we know the side length, we can substitute it into the formula:
A = (3^2 * √3) / 4
A = (9 * √3) / 4
To simplify this further, we can multiply 9 and √3 first:
A = (9√3) / 4
Now, we have the final answer for the area of the equilateral triangle:
A = (9√3) / 4 square inches
To find the area of an equilateral triangle with a given perimeter, you need to first find the length of each side of the triangle. Since an equilateral triangle has three equal sides, you can divide the perimeter by 3 to get the length of each side.
In this case, the given perimeter is 9 inches. Dividing it by 3, you get 3 inches as the length of each side.
Now, to find the area of the equilateral triangle, you can use the formula:
A = (√3/4) * s²
Where A is the area, s is the length of each side.
Plugging in the values, we have:
A = (√3/4) * 3²
A = (√3/4) * 9
Now calculate the value:
A ≈ 3.897 sq. in. (rounded to three decimal places)
So, the approximate area of the equilateral triangle is 3.897 square inches.