what is the area (in square units) of the triangle described?
1. a = 1, b = 1, c = 1
since it is equilateral, just recall that for a side length s,
area = √3/4 s^2
To find the area of a triangle, you can use the formula for the area of a triangle:
Area = (base * height) / 2
However, in order to use this formula, we need to know the length of the base and the height of the triangle. Since you have given the lengths of the triangle's sides (a, b, and c), we can use the Heron's formula to calculate the area of the triangle.
The Heron's formula states that the area of a triangle with sides of lengths a, b, and c is given by:
Area = √(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
In this case, a = 1, b = 1, and c = 1. We can substitute these values into the formulas to find the area.
First, calculate the semi-perimeter:
s = (1 + 1 + 1) / 2 = 1.5
Now, substitute the values of a, b, c, and s into the Heron's formula to find the area:
Area = √(1.5 * (1.5 - 1) * (1.5 - 1) * (1.5 - 1))
= √(1.5 * 0.5 * 0.5 * 0.5)
= √(0.5625)
≈ 0.75
Therefore, the area of the triangle described with sides a = 1, b = 1, and c = 1 is approximately 0.75 square units.