Question

Find the area of the the regular polygon.

Answer 1

Answer:

Area of Regular Polygon = ( About ) 332.6 units^2; Option C

Step-by-step explanation:

~ Let us first declare consecutive notes. If we were to draw an altitude in this triangle, it would be perpendicular to the base, by definition. At the same time this shape is a regular polygon, so all sides ( and angles ) are ≅. This would mean that, by Coincidence Theorem, the altitude divides the base into the two ≅ parts. ~

1. If that is so, the altitude would split this base into parts ⇒ ( 16√3 )/2 = 8√3.

2. This would mean that the altitude can be found through Pythagorean Theorem, provided that by definition it forms a 90 degree angle at the base. Let us say x ⇒ the length of the altitude, ( 8√3 )^2 + ( x )^2 = ( 16√3 )^2 ⇒ 192 + x^2 = 768 ⇒ x^2 = 576 ⇒ length of altitude - 24 units

3. With the base 16√3 units, and the the altitude/height 24 units, we can find the area of this regular polygon to be ⇒ 1/2 * base * height ⇒ 1/2 * 16√3 * 24 ⇒ 192√3 units^2

4. That being said that area would be 192 * 1.732050808...... ⇒

Area of Regular Polygon = ( About ) 332.6 units^2