An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nea

Question

1 year ago

7

rest tenth,
what is the area of the screw head?

1 answer:

Lunna [17] · Answer 1 · 2023-02-16T19:13:43+03:00

Given that the screw is a regular hexagon with side length 6 mm, the area of the screw is 93.5 mm^2

<h3>How can the area of the screw be found?</h3>

The area of an hexagon can be found using the following equation;

$A = \mathbf{ \frac{3 \cdot \sqrt{3} }{2} \times {a}^{2}}$

Where <em>a </em>= 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 <em>a </em>= 6, we have;

$A = \frac{3 \cdot \sqrt{3} }{2} \times {6 \: mm}^{2} = 93.5 \: mm^2$

Learn more about finding the area of an hexagon here:

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