2. (05.03 MC)
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 10.4 inches and the length of each side is 12 inches.

A hexagon labeled ABCDEF is shown will all 6 sides equal in length. ED is labeled as 12 inches. A perpendicular is drawn from the center of the hexagon to the side ED. This perpendicular is labeled as 10.4 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)

Answer is in the file below

cutt.ly/tz3yDpb

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3