The total area of the shaded regions is 8√3 m².
The three triangles along segment CD are all equilateral triangle and congruent with each other. If side CD measures 12 meters, then the side of each equilateral triangle is 4 meters.
length of each side of these three triangles = 12/3 = 4 m
Note that all the interior angles of an equilateral triangle is equal to 60°. So the two shaded triangles are also equilateral triangles with side equal to 4 meters.
Solve for the height of the equilateral triangle using Pythagorean theorem.
c² = a² + b²
4² = a² + (4/2)²
a² = 12
a = 2√3
height = 2√3 m
Solve for the area of the shaded region (2 equilateral triangle) using the formula in finding the area of a triangle.
total are of the shaded region = 2(1/2 bh)
total are of the shaded region = 2(1/2)(4 m)(2√3 m)
total are of the shaded region = 8√3 m²
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