It is -12,10 and your welcome for me helping you im only trying to get the point s
Answer:
0.24930286...
Step-by-step explanation:
Answer:
the area of the hexagon is approx. 187.1 in²
Step-by-step explanation:
Picture this regular polygon as being a hexagon made up of six equilateral triangles of side 12 in. We find the area of one such triangle and then multiply that by 6 to obtain the total area of the hexagon.
One such equilateral triangle has three sides all of length 12 in, and all the interior angles are 60°. The height of one such triangle is
h = (12 in)sin 60°, or
√3
h = (12 in) -------- = 6√3 in
2
So, with base 12 in and height 6√3 in, the area of one such equilateral triangle is
A = (1/2)(12 in)(6√3 in) = 36√3 in²
and the total area of the hexagon is 6(36)√3 in², or approx. 187.1 in²
There are two probabilities of the solution. First if 80° acts as one of the leg angles, second if 80° acts as the vertex angle.
FIRST PROBABILITY
If 80° is one of the leg angles, then the other angle would be 80° too, because iscosceles has two congruent angles on the leg.
Find the vertex angle
the sum of interior angles in a triangle is 180°
vertex angle + angle on the leg + angle on the leg = 180°
vertex angle + 80° + 80° = 180°
vertex angle + 160° = 180°
vertex angle = 180° - 160°
vertex angle = 20°
The interior angles are 80°,80°,20°
SECOND PROBABILITY
If 80° is the vertex angle, we should find the value of the two leg angles. The two legs has congruent angles.
Find the leg angles
the sum of interior angles in a triangle is 180°
leg angle + leg angle + vertex angle = 180°
2 × leg angle + vertex angle = 180°
2 × leg angle + 80° = 180°
2 × leg angle = 180° - 80°
2 × leg angle = 100°
leg angle = 50°
The interior angles are 80°, 50°, 50°
