We are asked to find the area of an equilateral triangle with a side length of 20 millimeters. Let's start by recalling the formula for the area of a triangle.
A = 1/2bh
In this formula, h is the height of the triangle and b is the length of the base of the triangle. We are given the side length, so we only need to find the height. Let's start by drawing our triangle.
Now that we have a diagram of the triangle, let's add the height. Since the triangle is equilateral, the two smaller triangles formed by the height are congruent. The shortest side is half as long as the side length of the equilateral triangle.
Let's focus our attention at one of the smaller triangles. It is a right triangle and one of its legs is missing.
For this right triangle, the lengths of the known leg and the hypotenuse are 10 and 120 millimeters, respectively. Let's substitute these values into the Pythagorean theorem and solve for the missing leg h.
Note that since h is the leg of a right triangle, it must be non-negative, which is why we only kept the principal root when solving the equation. The length of the hypotenuse is 110 sqrt(3) millimters. Now that we know both the height and the base, we can substitute them into the formula for the area of the triangle.
