A hexagon is made of six equilateral triangles. Each triangle area is 18 sq ft. Which value in feet most closely estimates the perimeter of such a hexagon?
Explanation
The area of the hexagon is the total of the area of its 6 equilateral triangles:
Area of hexagon \(= 6 \times 18 = 108\) square feet
For estimating purposes, you may assume the area of a hexagon to be close to the area of a circle (polygons of 5 sides or more approach the shape of a circle), and use the formula for circles.
\(\text { Area }=\pi / 4 \times D^{2}\)
\(108 \times 4 / \pi=D^{2}\)
\(D^{2}\) = 144 using \(\pi=3\)
D = 12
Compute for perimeter, using the Circle’s formula for perimeter or circumference:
\(P = pi \times D\)
\(= 3 \times 12 = 36\)
TIP: Use pi = 3 for approximations involving small numbers.
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