The perimeter of the base of a regular quadrilateral prism is 32 cm. The height of the prism is 2 times greater than the length of the base edge. Find the sum of all edges of the prism.
Accepted Solution
A:
Answer:The sum of all edges of the prism is 128 cm.Step-by-step explanation:It is given that the perimeter of the base of a regular quadrilateral prism is 32 cm. It means the base of the prism is a square.Let the length of the base edge be a.Perimeter of a square is 4a.[tex]4a=32[/tex]Divide both sides by 8.[tex]a=8[/tex]The length of base edge is 8. It is given that the height of the prism is 2 times greater than the length of the base edge. It means the height of the prism is [tex]2\times 8=16[/tex]The sum of all edges of the prism is[tex]P=4(length+breadth+height)[/tex]Length and breadth of the prism is 8 cm and height of the prism is 16 cm.[tex]P=4(8+8+16)[/tex][tex]P=4(32)[/tex][tex]P=128[/tex]Therefore the sum of all edges of the prism is 128 cm.