Answer:
456.2 units²
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