Answer:
D. 28 square centimeters
Step-by-step explanation:
The surface area of the prism is the sum of the base areas and the lateral area. Here, the base is an odd shape, so it must be decomposed into shapes we can find the area of.
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<h3>base area</h3>
The base of this prism is the L-shaped face nearest the observer. It can be decomposed into a 1 cm square atop a 1 cm by 3 cm rectangle. The area of the face is the sum of the areas of these parts.
square area = s² . . . . where s is the side length
= (1 cm)² = 1 cm²
rectangle area = bh . . . . b is the base, h is the height
= (3 cm)(1 cm) = 3 cm²
Then the area of the one prism base we see is ...
base area = 1 cm² +3 cm² = 4 cm²
The total area of both L-shaped bases of the prism is ...
total base area = 2(4 cm²) = 8 cm²
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<h3>lateral area</h3>
The perimeter of the base is the sum of the lengths of its edges. Working clockwise from the lower left corner, we find the base perimeter to be ...
(1 +2 +1 +1 +2 +3) cm = 10 cm
The lateral area is the product of the "height" of the prism (the distance between the parallel bases) and this perimeter length.
LA = Ph
LA = (10 cm)(2 cm) = 20 cm²
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<h3>solid area</h3>
The surface area of the solid is the sum of the areas of the bases and the lateral area:
total surface area = total base area + LA
= (8 cm²) +(20 cm²) = 28 cm²
The surface area of the solid is 28 square centimeters.
