If w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? Round your answer to the nearest tenth. 656.2 units2
400 units2
256.2 units2
456.2 units2

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

w

step-by-step explanation: