Given that the screw is a regular hexagon with side length 6 mm, the area of the screw is 93.5 mm^2
How can the area of the screw be found?
The area of an hexagon can be found using the following equation;
[tex]A = \mathbf{ \frac{3 \cdot \sqrt{3} }{2} \times {a}^{2}} [/tex]
Where a = The side length
However the side lengths are not equal, and the figure is a composite figure with two triangles and one rectangle;
Base length of the triangles = 12
Height of the triangles = 3
Area of each triangle = 0.5 × 12 × 3 = 18
Width of the rectangle = 12
Height of the rectangle = 6
Area of the rectangle = 12 × 6 = 72
Area of the screw = 18 + 18 + 72 = 108
However taking the screw as a regular hexagon, with side length a = 6, we have;
[tex]A = \frac{3 \cdot \sqrt{3} }{2} \times {6 \: mm}^{2} = 93.5 \: mm^2 [/tex]
- The correct option is D. 93.5 mm^2
Learn more about finding the area of an hexagon here:
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