What is the perimeter of a polygon abcd vertex a(5,12) b(9,9) c(12,5) d(0,0)
1 answer:
Answer:
36
Step-by-step explanation:
We have to compute 4 distances and then add them up.
It may help to draw this first to see which distances to compute.
So I'm going to start with computing the distance from (0,0) to (5,12), then from (5,12) to (9,9), then from (9,9) to (12,5), and then finally from (12,5) to (0,0).
So distance from (0,0) to (5,12)
d=sqrt((5-0)^2+(12-0)^2)=sqrt(25+144)=sqrt(169)=13
Distance from (5,12) to (9,9)
d=sqrt((9-5)^2+(12-9)^2)=sqrt(4^2+3^2)=sqrt(16+9)=sqrt(25)=5
Distance from (9,9) to (12,5)
d=sqrt((12-9)^2+(9-5)^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5
Distance from (12,5) to (0,0)
d=sqrt((12-0)^2+(5-0)^2)=sqrt(12^2+5^2)=sqrt(144+25)=sqrt(169)=13.
Up all of our distances 13+5+5+13=(13+13)+(5+5)=26+10=36
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so.. notice, the box for the gift is really just a rectangular prism, which is really just 6 rectangles stacked up to each other at the edges.
the front and back are two 5x3 rectangles
the left and right are just two 3x7 rectangles
and the top and bottom are just two 5x7 rectangles
so, just get the area of each, sum them up, and that's the area of the rectangular prism and thus of the box, and that's how many in² she will need.
Answer:
144
Step-by-step explanation: