I WILL GIVE 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 8.7 inches and the length of each side is 10 inches. A hexagon labeled ABCDEF is shown will all 6 sides equal in length. ED is labeled as 10 inches. A perpendicular is drawn from the center of the hexagon to the side ED. This perpendicular is labeled as 8.7 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)

Step-by-step explanation:

Part A:

The area can be decomposed into triangles by drawing a line from the center to each vertex of the hexagon.

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Part B:

The area of each triangle is given by the triangle area formula:

  A = (1/2)bh

  A = (1/2)(10 in)(8.7 in) = 43.5 in²

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Part C:

The area of the table top is 6 times the area of one triangle:

  surface area = 6(43.5 in²) = 261 in²

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation: