Rebecca brought a jewelry box in the shape of an octagon. She wants to put a net over the lateral faces of the box.

Question

Find the lateral area of the jewelry box. (JUSTIFY)

Answer 1

Every prism has s lateral faces and 2 bases, where s is the number of sides on the base. A triangular prism has 3 lateral faces and 2 bases. So 5 total.

Lateral faces are the faces in a prism or pyramid that are not bases.

Given these definitions, Rebecca's jewelry box has 8 lateral faces (it is an octagon), and 2 bases (a top and a bottom).

Assuming that the shape of the box is a regular octagon, there are eight 5"x2" rectangles (the sides) that will be covered. That is, 8 * 5" * 2" = 80 square inches.

CAUTION: This may be a "trick" question or else it is easily misunderstood.

Answer 2

α=22.5º

β=67.5°

γ=90°

a=1"

a/sinα=c

1/.383=2.613=c

c^s-a^2=b^2

6.828-1=5.828; b=2.414

ab2=triangle*8=octagon=38.627sq/in

volume=38.627*5=193.137cu/in

area=2a*5*8+2*38.627=157.254sq/in

Answer 3

Draws the 8 segments from the center to each vertex. 8 congruent triangles are formed each with base angles 62.5

In each, the perpendicular height from center to edge is found as 1/cos(62.5)= 1.92

The area of the octogon is 15.36

The total surface area is then 95.36 not counting the bottom