Find the perm of shaded shape
1 answer:
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Answer:
SA = 1244.64 square centimeters
Step-by-step explanation:
From the attached figure
The formula of the surface area of the prism is SA = 2B + PH, where
- B is the area of its base
- P is the perimeter of its base
- H is the distance between its bases
The base of the prism is a regular hexagon with side 8 cm
If you join each vertex of the hexagon with its center you will form 6 congruent triangles with base 8 cm and height 6.93 cm
The area of the hexagon = 6 × area of a triangle
∵ The base of the triangle = 8 cm
∵ Its height = 6.93 cm
- The formula of the area of a triangle is A = × base × height
∴ Area of the triangle = × 8 × 6.93 = 27.72 cm²
- Lets find the area of the hexagon
∴ The area of the hexagon = 6 × 27 .72 = 166.32 cm²
∴ B = 166.32 cm²
The formula of the perimeter of the regular hexagon is P = 6 × s, where s is the length of its side
∵ The side of the hexagon is 8 cm
∴ P = 6 × 8
∴ P = 48 cm
∵ The distance between the two bases is 19 cm
∴ H = 19 cm
Substitute the values of B, P and H in the formula of the surface area above
∵ SA = 2(166.32) + (48)(19)
∴ SA = 332.64 + 912
∴ SA = 1244.64 square centimeters
