Answer:
1570 in²
Explanation:
You want the total surface area of the irregularly-shaped prism shown.
Dimensions
The single hash mark on some segments indicates those are all the same length (congruent). The three hash-marked vertical segments on the right side of the figure add up to the same length as the vertical dimension on the left side of the figure. If each of those hash-marked segments is 'x', then we have ...
3x = 15
x = 5 . . . . . divide by 3
The dimensions of the base edges of the figure can now be seen to match those shown in the attachment.
Base area
The shaded front face (base) of the prism has overall dimensions of 15 inches high by 5 +11 = 16 inches wide. That's an area of ...
A = BH = (16 in)(15 in) = 240 in²
From that area we can subtract rectangles from the upper right and lower right to find the shaded area. Those rectangles have a total area of ...
upper right + lower right = (4 in)(5 in) +(11 in)(5 in) = (20 +55) in² = 75 in²
Then the shaded base (front face) area is ...
A = (240 in²) -(75 in²) = 165 in²
The back face is identical in shape and area, so the total base area of the prism is ...
Base area = 2 × 165 in² = 330 in²
Lateral area
The total area of the rectangular faces is the product of the perimeter of the base and the distance between the two bases.
The perimeter is (working clockwise from lower left) ...
15 in +12 in +5 in +4 in +5 in +11 in +5 in +5 in
= 62 in
Then the lateral area is ...
LA = Ph = (62 in)(20 in) = 1240 in²
Surface area
The surface area is the sum of the base area and the lateral area:
SA = B +LA = 330 in² +1240 in² = 1570 in²
The surface area of the shape is 1570 square inches.
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Additional comment
In effect, the perimeter is the sum of the lengths of horizontal edges and vertical edges. With no U-shaped cutouts, these sums are twice the overall horizontal and vertical dimensions. Here, that is ...
2(16 in +15 in) = 2(31 in) = 62 in
This is an easier computation than adding the individual side lengths.