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GEOMETRY HOMEWORK HELPP????!!!!!?
When a vertex is cut from a solid, it is said to be truncated. (think of the pedestal a tiger stands on at the circus, or a reese's peanut butter bup.) A 20 inch tall hexagonal pyramid with a side length of 4 inches is truncated to half its original height. What is the surace area of the resulting truncated hexagonal pyramid? Perform all calculations to recieve any credit. Show all calculations/drawings.
2 Answers
- SueLv 79 years agoFavorite Answer
Draw a picture of the hexagonal base.
The base is a hexagon. the central angle in a hexagon is 360 /6= 60 degrees per sector.
Look at a single sector of the base. It is an isosceles triangle 4 inches to a
side and a radius of 4, the apothem would bisect the side leaving us with a 30-60-90 triangle.
The side opposie the 30=2 and the hypotenuse is 4 leaving the apothem to be 2√3.
Area of a regular polgon = 1/2*a*P
The apothem(a) = 2√3 in
draw a picture of your prism.
The Perimeter(P) = 6*4= 24 in
A= 1/2*2√3*24= 24√3 in²
The Surface area of a right prism = area of 2 bases + perimeter of the base times the height.
SA= 2(24√3) + 24*10= 48√3 +240 = 323.14 in²
- ?Lv 69 years ago
Sides area=6*4*10=240
Hexagonal has 'height'=2(3)^1/2
One end area = 2(3)^1/2*2*6
Two ends=2(3)^1/2*2*6*2=83.14
Total area=240+83.14=323.14 sq in
