Question

What’s the area of the triangle

Answer 1

A= 173.2mm².

Explanation:

1. Find hidden values for the triangle.

a) We are told that the triangle is equilateral, which means that all sides have the same length. Therefore, all sides are 20mm long.

b) If a triangle is equilateral, then all it's inner angles have the same measure. The total measure of all inner angles in a triangle is 180°. Since they are 3 and all measure the same, they all measure 60° (180°/3).

Check these notes on attached image 1.

2. Get more data.

We are told to calculate the area of this triangle, here's the formula for the area of a triangle:

`A=(bh)/(2)`

As you can tell, this formula depends on the length of the base of the triangle, and its height. We don't have the height, so we'll have to calculate it. In order to make this, check step 3.

3. Draw an imaginary line in the middle of the triangle to create a rectangle triangle and annotate the new created angles.

Check attached image 2.

4. Calculate the height of the red line using trigonometry functions.

From the 60° angle, we may use the "sine" function to calculate the height:

`Sin(x)=(Opposite)/(Hypotenuse)\\ \\Sin(60)=(x)/(20mm)`

Check attached image 3.

Solve for "x" and calculate:

`Sin(60)=(x)/(20mm)\\ \\x=Sin(60)*20mm\\ \\x=17.32mm`

5. Use the data to find the area.

Check attached image 4.

`A=((20mm)(17.32mm))/(2) \\ \\A=173.2mm^(2) .`