If w = 10 units, x= 5 units, and y= 6 units, what is the surface area of the figure?

  456.2 units²

Step-by-step explanation:

The area of the square base is ...

  base area = w² = (10 units)² = 100 units²

The lateral area is 4 times the area of one rectangular face:

  lateral area = 4wx = 4(10 units)(5 units) = 200 units²

The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:

  h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²

  h = √61 units

So, the area of 4 triangles is ...

  area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²

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Now we have the areas of the parts, so we can add them together to get the total surface area:

  surface area = base area + lateral area + area of triangular faces

  = 100 units² + 200 units² + 156.2 units²

  surface area = 456.2 units²

75%

step-by-step explanation: