Answer:
162 square units
Explanation:
You want the surface area of the trapezoidal prism.
Base area
The triangle at the top of each base is a right triangle with leg 3 units and hypotenuse 5 units. This tells you it is a 3-4-5 right triangle and the width of the prism is 4 units.
The area of each trapezoidal base is ...
A = 1/2(b1 +b2)h = 1/2(3 +6)(4) = 18 . . . . . square units
Lateral area
The lateral area is the product of the height of the prism (7) and the perimeter of the base. The vertical edges of the base are 3 and 6, the horizontal edge is 4 (see above), and the slant edge is shown as 5. This means the perimeter is 3+6+4+5 = 18 units.
The lateral area of the prism is ...
LA = Ph = (18)(7) = 126 . . . . . square units
Total surface area
The total surface area of the prism is the sum of the areas of the two bases and the lateral area:
2(18) +126 = 162 . . . . . . square units
The surface area of the composite solid is 162 square units.
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Additional comment
If you have forgotten about the 3-4-5 right triangle, you can find the missing side length using the Pythagorean theorem.
a² +b² = c²
3² +b² = 5²
b² = 25 -9 = 16
b = √16 = 4 . . . . . . the missing triangle side is 4 units long
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