Question

The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is 7.8 inches and the length of each side is 9 inches.
A hexagon labeled ABCDEF is shown will all 6 sides equal in length. ED is labeled as 9 inches. A perpendicular is drawn from the center of the hexagon to the side ED. This perpendicular is labeled as 7.8 inches.


Part A: Describe how you can decompose this shape into triangles. (2 points)


Part B: What would be the area of each triangle? Show every step of your work. (5 points)


Part C: Using your answers above, determine the area of the table's surface. Show every step of your work. (3 points)

pls hurry

Answer 1

A) Add three line segments (AD, CF, BE) to the regular hexagon.

B) The area of each triangle of the regular hexagon is 35.1 in².

C) The area of the regular hexagon is 210.6 in².

How to calculate the area of a regular hexagon

In geometry, regular hexagons are formed by six regular triangles with a common vertex. We decompose the hexagon in six equilateral triangles by adding three line segments (AD, CF, BE).The area of each triangle is found by the following equation:

A = 0.5 ·  (9 in) · (7.8 in)

A = 35.1 in²

And the area of the regular polygon is six times the former result, that is, 210.6 square inches.

To learn more on polygons: brainly.com/question/17756657

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