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? (5 points) part c: using your answers above, determine the area of the table's surface. (3 points)

A. To decompose this shape into triangles, you would connect the centerpoint to each vertex. In the picture the orange lines are used to create the triangles. You were able to create six congruent triangles.

B. To find the area of one of the triangles, you will use the formula for finding area of a triangle. See the work the side B. One triangle has an area of 35.1 in.².

C. To find the total area of the table surface, you would multiply 35.1 in.² by 6 because there are six triangles that are exactly the same. The total area is 210.6 in.².

Good luck!

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simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .