Answer:
area = 1217.16 in²
Explanation:
a nonagon has 9 sides
each side = 126/9 = 14 inches
it forms 9 identical isosceles triangles with a base of 14
each top angle = 360/9 = 40°
the area of each triangle can be found by the formula area = 1/2(base)(height)
We know the base is 14
the height would be calculated be constructing a perpendicular line from the top of the triangle and perpendicular to the base. This smaller triangle base is 1/2 of 14, or 7 inches. it's top angle is 1/2 of 40°, or 20°
the height of smaller triangle is the same height as the larger triangle.
tan 20° = 7/height
0.3640 = 7/x
0.3640height = 7
height = 19.32 inches
area of larger triangle = 1/2(14)(19.32) = 135.24 in²
total area = 9 x 135.24 = 1217.16 in²