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.
The sum of all edges of the regular quadrilateral prism in which the perimeter of the base of prism is 32 cm, is 128 cm.
The measure of the boundary of a plane or shape is called its perimeter. The perimeter of a plane or shape is the sum of all the sides.
The perimeter of the base of a regular quadrilateral prism is 32 cm. For the regular quadrilateral, the length of each 4 side of base is equal. Let the length of side of base is l. Thus,
[tex]4\times l=32\\l=\dfrac{32}{4}\\l=8\rm\; cm[/tex]
The height of the prism is 2 times greater than the length of the base edge. Thus, the height of the prism is,
[tex]h=2\times8\\h=16\rm\; cm[/tex]
There is total 8 base side edges with equal length and 4 edges which is equal to length of height. Thus, the sum of all edges of the prism is,
[tex]\sum s=8\times8+4\times16\\\sum s=64+64\\\sum s=128\rm\; cm[/tex]
Thus, the sum of all edges of the regular quadrilateral prism in which the perimeter of the base of prism is 32 cm, is 128 cm.
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