Question

Find the area of the head using each persons method. Show your reasoning.

Answer 1

The area of the hexagonal head using each persons (Andre & Lin) method is;

Total Area using Lin's method = 93.6 ft²

Total Area using Andre's method = 93.6 ft²

• 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

• B) Andre's method;

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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