Stephan has a box in the shape of a hexagonal prism where the hexagonal bases are regular. a net of the box is below.
figure 1

he measured the height of the box to be 6 in. then, stephan drew a line from the center of one of the hexagons to each of its vertices and noticed that all the triangles he created have a height of 7 in and a base of 8 in.

note: figure is not drawn to scale.

what is the surface area of the hexagonal prism?
a. 912 sq in
b. 624 sq in
c. 456 sq in
d. 480 sq in

The answer is B:  624 sq. in

Step-by-step explanation:

find the area of one hexagons

since there are 6 congruent triangles, you find the area of 1 of the triangles and multiply by 6

Area of 1 triangle:

1/2bh = 1/2 (8 in) (7 in)

=1/2 (56 sq in.)

= 28 sq in.

Area of 1 hexagon is 6 (28 sq. in) = 168 sq. in.

There are 2 hexagons in the net, so multiply by 2

Area of 2 hexagons is...

2 (168 sq. in) = 336 sq. in.

Then find the area of the rectangular sides...which will be the 6 small squares shown on the first picture

**the rectangles each have 1 side that is equal to 1 side of the hexagon and 1 side is equal to the height of the prism.

Area of 1 rectangle side

lw = (8 in) (6 in.)

= 48 sq. in.

multiply all of the 6 sides of the area

=6 (48 sq.in)

=288 sq. in

Then add the area of the 2 hexagons to the area of the 6 rectangular sides

Total area = 336 sq. in + 288 sq. in

= 624 sq. in.

d

step-by-step explanation:

d

2 is the final ! : )