Answer:
D. 456.2 units2
Step-by-step explanation:
Find the area of all 4 sides of cuboid
Area of rectangle = length x breadth
Area of rectangle = 10 x 5
=50 Units^2
There are 4 rectangles
Area of 4 rectangles =4*50
= 200 Units^2
Calculate bottom of cuboid
Area = length x breadth
Area = 10 x 10
Area = 100 Units^2
Find the slant height of pyramid
Using Pythagoras theorem
c² = a² + b²
Where,
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
=25+36
c²=61
c = √61
Find area of face of the pyramid by finding the area of a triangle
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 10 x √61
Area of triangle = 5√61
There are 4 faces in the pyramid
Area of 4 triangles =4 * 5√61
= 20√61
Total surface area=Area of 4 rectangles + Area of the bottom of a cuboid + Area of 4 faces of the pyramid
Total surface area = 200 + 100 + 20√61
Total surface area = 456.2 units^2