Answer:
1240.4 mm²
Explanation:
SA of Pentagonal pyramid:
(as)(5/2) + (sl)(5/2)
↑ ↑
base area lateral area
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a: apothem (in-radius) length, s: side length.
l: slant height.
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Since we are already given the base area which is 440.4 mm². All we need to do is find the lateral area and add both areas together.
Given that the triangular face of the lateral part has a side/base length of 16mm, and a 20mm slant height.
A triangle has an area of ½bh and since there are 5 of these faces total, (5)(½bh) = (5/2)(bh). In a three dimensional perspective, b will be s and h will be l so (sl)(5/2).
With this information the surface area is:
(16)(20)(5/2)mm + (440.4 mm²) →
800 mm² + 440.4 mm² =
1240.4 mm²