Answer:
128 + 96√3 or 294.28 unit^3 to the nearest hundredth.
Step-by-step explanation:
The surface area of one of the pyramids = area of the square base + area of the 4 equilateral triangles
= 8^2 + 4 * 1/2 * 8 * 4√3
= 64 + 64√3.
So the area of the new solid = 2(64 + 64√3) - area of 2 triangles
= 2(64 + 64√3) - 32√3
= 128 + 128√3 - 32√3
= 128 + 96√3.
The surface area of the new figure is given by the sum of the surface area of the exposed surface.
The surface area of the new solid is 128 + 96·√3 square units.
Reason:
The given parameters are;
The side length of the base of the square pyramid = 8
Area of each triangular surface = 0.5 × 8 × 8 × sin(60°) = 16·√3
The area of the six exposed triangular surfaces of the new solid is given as follows;
A₆ = 6 × 16·√3 = 96·√3
Area of the two square bases, [tex]A_{sb}[/tex] = 2 × 64 = 128
The surface area of the new solid, A = [tex]A_{sb}[/tex] + A₆
∴The surface area of the new solid, A = 128 + 96·√3 square units
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