Please need help very quickly!

Question

Question 1: A regular hexagonal prism has a height of 7 cm and base edge length of 4 cm. Identify its lateral area and surface area.

A.) L = 168 cm² ; S = 251.1 cm²

B.) L = 168 cm² ; S = 209.6 cm²

C.) L = 158 cm² ; S = 251.2 cm²

D.) L = 178 cm² ; S = 209.6 cm²

Question 2: Identify the distance between points (3,8,0) and (−2,9,−4), and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary.

A.) d ≈ 6.5 units; M (−0.5, 8.5, 2)

B.) d ≈ 3.5 units; M (0.5, 8.5, −2)

C.) d ≈ 6.5 units; M (0.5, 8.5, −2)

D.) d ≈ 3.5 units; M (−0.5, 8.5, 2)

Answer 1

Again, Lateral Area is the combined area of all FACES. In this case, these are 6 congruent RECTANGLES, each with dimensions of 4x7. So LA would be 6x(4x7).

Then, to find SA, you must add the answer you found above, to the combined areas of BOTH BASES, which are regular hexagons of side length 4. The cool thing about a regular hexagon, is that it can be split up into 6 congruent equilateral triangles! That makes finding its area easy! Just find the area of one of those triangles - perhaps needing to find the apothem (perpendicular distance from the center of a regular polygon to one edge) with the pythagorean theorem or by knowledge of special 30-60-90 right triangles - and multiply by 6.