To find the area of the regular hexagon, we need to first find the length of each side. Since the hexagon is regular, all sides are equal in length.
Using the Pythagorean theorem, we can find the length of one side:
a^2 + (b/2)^2 = s^2
13^2 + (16/2)^2 = s^2
169 + 64 = s^2
233 = s^2
s ≈ 15.26 inches
Now that we know the length of one side, we can use the area formula for triangles to find the area of one of the six equilateral triangles that make up the hexagon:
A = (1/2)bh
A = (1/2)(15.26)(13)
A ≈ 99.2 square inches
Since there are six of these triangles in the hexagon, we can find the total area by multiplying by 6:
Total area = 6A
Total area ≈ 595.2 square inches
Therefore, the area of the regular hexagon is approximately 595.2 square inches.
Find the area of the regular hexagon below by using the area formula for triangles.
a = 13 inches and b = 16 inches
*picture not drawn to scale
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