Question

8 nora has a craft box that is a right hexagonal prism. the line segment labeled 2.6 inches begins at the center of the hexagon and ends at one side of the hexagon. she removes the latch and paints the outside surface except for the bottom. how many square inches does she paint?

Explanation:

Step1: Calculate 1 hexagon area

A regular hexagon can be split into 6 equilateral triangles. The area of one triangle is $\frac{1}{2} \times 4 \times 2.6$, so the area of 1 hexagon is:
$$6 \times \frac{1}{2} \times 4 \times 2.6 = 31.2 \text{ sq in}$$

Step2: Calculate lateral surface area

The lateral surface area is 6 rectangular faces, each with area $4 \times 3$:
$$6 \times 4 \times 3 = 72 \text{ sq in}$$

Step3: Sum painted top + lateral area

We exclude the bottom hexagon, so total area before subtracting latch:
$$31.2 + 72 = 103.2 \text{ sq in}$$

Step4: Subtract latch area

The latch is a rectangle with area $4 \times 3$:
$$103.2 - (4 \times 3) = 103.2 - 12 = 91.2 \text{ sq in}$$

Answer:

91.2 square inches