The area of the hexagonal head using each persons (Andre & Lin) method is;
<u><em>Total Area using Lin's method = 93.6 ft²</em></u>
<u><em>Total Area using Andre's method = 93.6 ft²</em></u>
- A) Lin's Method; From division of polygons , we know that a regular hexagon can be divided into 6 equilateral triangles.
From the image, a side of the hexagon is 6 inches. This means that all sides of each triangle will be also 6 inches.
Formula for area of a triangle = ¹/₂(base x height)
We see a perpendicular distance spanning from one end of the hexagon to the other end passing through the centre of the hexagon. It passes 2 triangles.
Thus, the height of one triangle = 10.4/2 ft = 5.2 ft
Area of one triangle = ¹/₂ × 6 × 5.2 = 15.6 ft²
Thus, Area of hexagon = area of 6 triangles = 6 × 15.6 = 93.6 ft²
Let us first find the area of the rectangle;
Area of rectangle = length × width
Area of rectangle = 10.4 × 6 = 62.4 ft²
For the rectangle, we know three sides now which are;
10.4 ft, 6 ft, 6 ft but we don't know the height and as such we will use heron's formula to get the area of one triangle;
A = √s((s - a)(s - b)(s - c))
where; a,b and c are the 3 sides of the triangle
s = (a + b + c)/2
Thus; s = (10.4 + 6 + 6)/2 = 11.2 ft
Thus;
A = √11.2((11.2 - 10.4)(11.2 - 6)(11.2 - 6))
A = 15.6 ft²
There are 2 triangles and so Area of 2 triangles =2 × 15.6 = 31.2 ft²
Thus;
Total Area = 62.4 ft² + 31.2 ft²
Total Area = 93.6 ft²
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to the nearest cent.