Question

the diagram shows the dimensions of a wooden block. the block will be covered with a reflective film. how much of the film is needed to cover the entire block?

Answer 1

This questions is asking for the Surface Area of the wooden block. To find Surface Area, you have to add up the area of every surface on the block: the two triangles on each end, the side, the bottom, and the angled top.

Triangles:
The area of a triangle is found with $\frac{1}{2}bh$, where b = base and h = height. For these triangles, the base is 3 and the height is 4, so you plug it in to get:
$\frac{1}{2}(3)(4) = 6$
However, there are two triangles with that area, so the total area is 6 x 2 = 12

Bottom:
The bottom has a length of 6 and a width of 3, so the area is 6 x 3 = 18

Side:
The side has a length of 6 and a height of 4, so the area is 6 x 4 = 24

Angled Side:
The angled side/top has a length of 6 and a width of 5 (remember, it's diagonal), so the area is 6 x 5 = 30.

Add up all of the areas to get 12 + 18 + 24 + 30 = 84 cm^2, or answer choice B.