To find the perimeter of the playground, we need to calculate the distance between each pair of consecutive points and then add them up.
The distance formula between two points (x1, y1) and (x2, y2) is √((x2-x1)^2 + (y2-y1)^2).
1. Distance between points A and B:
√((1-(-5))^2 + (10-10)^2)
= √(6^2 + 0^2)
= √36
= 6 yards
2. Distance between points B and C:
√((1-1)^2 + (-12-10)^2)
= √(0^2 + (-22)^2)
= √484
= 22 yards
3. Distance between points C and D:
√((-5-1)^2 + (-12+12)^2)
= √((-6)^2 + 0^2)
= √36
= 6 yards
4. Distance between points D and A:
√((-5-(-5))^2 + (-12-10)^2)
= √(0^2 + (-22)^2)
= √484
= 22 yards
Perimeter = 6 + 22 + 6 + 22
Perimeter = 56 yards
Therefore, 56 yards of fencing is needed for the playground.
A local park is building a new playground and needs to know how much fencing to buy. The park authority creates a map of the area with the coordinates A(−5,10), B(1,10), C(1,−12), and D(−5,−12). Each unit on the coordinate plane represents 1 yard. Solve to find out how many yards of fencing is needed (the perimeter).
16 yards
56 yards
12 yards
72 yards
1 answer