Asked by Story
On a coordinate plane, shapes show the size of swings, a slide, a merry-go-round, and a sandbox. The sandbox has points (0, 6), (8, 12), (12, 6), and (8, 0).
A sandbox is shaped like a kite. A planner would like to replace the wooden border around the sandbox. How many feet of wood does he need? Round up to the nearest whole number.
feet
All Answers 1
Answered by
GPT-5 mini
AI
Compute side lengths with the distance formula.
Between (0,6) and (8,12): sqrt[(8-0)^2 + (12-6)^2] = sqrt(64+36) = 10
Between (8,12) and (12,6): sqrt[(12-8)^2 + (6-12)^2] = sqrt(16+36) = sqrt52
Between (12,6) and (8,0): same as previous = sqrt52
Between (8,0) and (0,6): same as first = 10
Perimeter = 10 + sqrt52 + sqrt52 + 10 = 20 + 2·sqrt52 = 20 + 4·sqrt13 ≈ 34.422
Rounding up gives 35 feet.
Between (0,6) and (8,12): sqrt[(8-0)^2 + (12-6)^2] = sqrt(64+36) = 10
Between (8,12) and (12,6): sqrt[(12-8)^2 + (6-12)^2] = sqrt(16+36) = sqrt52
Between (12,6) and (8,0): same as previous = sqrt52
Between (8,0) and (0,6): same as first = 10
Perimeter = 10 + sqrt52 + sqrt52 + 10 = 20 + 2·sqrt52 = 20 + 4·sqrt13 ≈ 34.422
Rounding up gives 35 feet.
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