Question

2 ignacio makes a display shelf from 4 wooden boards. all angles boards are right angles. ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. what is the total area ignacio will stain? show your work. 32 in. 7 in. 9 in. 30 in. 4 in.

Explanation:

Step1: Identify outer surface areas (excl. back)

First, calculate the outer front/top/bottom/right/left areas:
Outer front/back area: $32 \times 9$ (we exclude back, so only front: $32 \times 9$)
Outer top/bottom: $2 \times (32 \times 4)$
Outer right/left: $2 \times (9 \times 4)$
Combined outer area (no back):
$32 \times 9 + 2 \times (32 \times 4) + 2 \times (9 \times 4)$
$= 288 + 256 + 72 = 616$ sq.in.

Step2: Calculate inner surface areas

Now find the inner exposed areas:
Inner top/bottom: $2 \times (30 \times 4)$
Inner right/left: $2 \times (7 \times 4)$
Inner front (the hollow part's front is already counted? No, the inner back is against wall, so we don't count it. The inner front is the frame's inner edge? Wait no, the inner faces are the ones inside the shelf:
Wait, the inner height is 7 in, inner length 30 in, depth 4 in.
Inner top/bottom: $2 \times (30 \times 4) = 240$
Inner right/left: $2 \times (7 \times 4) = 56$
Inner front (the vertical strip of the frame's inner front? No, the outer front is the full 32x9, and the hollow part is 30x7, so the front frame area is already included in the outer front. We just need the inner side walls.
Total inner area: $240 + 56 = 296$ sq.in.

Step3: Sum all stainable areas

Add outer (no back) and inner areas:
$616 + 296 = 912$

Answer:

912 square inches