# Lin and Andre used different methods to find the area of a regular hexagon with 6-inch sides. Lin decomposed the hexagon into six

Question

Lin and Andre used different methods to find the area of a regular hexagon with 6-inch sides. Lin decomposed the hexagon into six identical triangles. Andre decomposed the hexagon into a rectangle and two triangles.

Find the area of the hexagon using each person’s method. Show your reasoning.

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3 weeks 2023-01-14T21:59:09+00:00 2 Answers 0 views 0

## Answers ( 2 )

1. Answer:
108inches^2
Step-by-step explanation
………………………………………
Divide the hexagon in identical triangles.
Triangle area = length × width / 2
6 × 6 = 36
36/2= 18

2. The area of a regular hexagon is 85.28 square inches.
Given that, Lin and Andre used different methods to find the area of a regular hexagon with 6-inch sides.
We need to find the area of a hexagon using both methods.

### What is the area of a regular hexagon?

The formula for the area of a regular hexagon is (3√3 s²)/2, where ‘s’ is the length of the side of the hexagon. Since we are talking about a regular hexagon, it should be noted that all sides are of equal length. When one side of the regular hexagon is known, the area can be calculated with the formula, Area of the hexagon = (3√3 s²)/2, where ‘s’ is the length of the side of the hexagon.
We know that, the area of an equilateral triangle=√3/2 × a².
So, the area of an equilateral triangle= √3/2 × 6²
=18√3 square inches
Now, the area of a hexagon=6×18√3
=108√3=187.06 square inches
Area of the rectangle = length × width = 10.4 × 6 = 62.4 square inches
Area of a triangle= 1/2 × Base × Height = 1/2 × 10.4 × 2.2 = 11.44 square inches
Now, 11.44 × 2=22.88
Area of a regular hexagon =  62.4+22.88 =85.28 square inches
Therefore, the area of a regular hexagon is 85.28 square inches.
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Your question is incomplete, probably the complete question/missing part is:
Lin and Andre used different methods to find the area of a regular hexagon with 6-inches sides. Lin decomposed the hexagon into six identical, equilateral triangles. Andre decomposed the hexagon into a rectangle and two triangles. Lin’s method Andre’s method Find the area of the hexagon using each person’s method. Show your reasoning.