To find the area of the sandbox, we need to calculate the area of the regular hexagon.
A regular hexagon can be divided into six congruent equilateral triangles. The area of an equilateral triangle can be calculated using the formula:
Area = (s^2 * √3) / 4,
where "s" is the length of each side.
In this case, the length of each side, s, is 40 inches.
Plugging in the values, we have:
Area of each equilateral triangle = (40^2 * √3) / 4
= (1600 * √3) / 4
= 400√3 square inches.
Since there are six equilateral triangles in a hexagon, the total area of the hexagon is:
Total area of hexagon = 6 * Area of each equilateral triangle
= 6 * 400√3 square inches
= 2400√3 square inches.
Thus, the area of Tess's sandbox, which is a regular hexagon with all sides measuring 40 inches, is 2400√3 square inches.
Tess builds a sandbox on the shape of a regular hexagon in which all sides are 40 inches long
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