Answer:
D:456.2 units²
Step-by-step explanation:
Step 1: Area of all 4 sides of cuboid
Area of rectangle = 4 x length x breadth
Area of rectangle = 4 x 10 x 5
Area of rectangle = 200
Step 2: Calculate bottom of cuboid
Area = length x breadth
Area = 10 x 10
Area = 100
Step 3: Calculate slant height of pyramid
c² = a² + b²
c² is hypotenuse
a² is the base which is half of w (10/2 = 5)
b² is y which is 6
c² = a² + b²
c² = 5² + 6²
c = √61
Step 4: Calculate area of one face of the pyramid
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 10 x √61
Area of triangle = 5√61
Step 5: Calculate areas of all 4 faces of the pyramid
4 x 5√61 = 20√61
Step 6: Calculate the total surface area
Total surface area = 200 + 100 + 20√61
Total surface area = 456.2
The surface area of the figure is 456.2 units²
Option D is correct.
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