Answer:
Perimeter: Approximately 25.78 units
Area: 45 square units
Explanation:
To calculate the perimeter and area of the lion sanctuary, we need to use the given coordinates of the vertices. Let's start by calculating the perimeter and then move on to the area.
Given Coordinates of Vertices:
E(1, 4), A(5, 7), D(1, 1), F(5, 4), B(8, 7), C(8, 1)
Calculate Perimeter:
Perimeter is the sum of all the sides of the polygon formed by the vertices.
Side lengths:
EA = √((5-1)^2 + (7-4)^2) = √(16 + 9) = √25 = 5
AD = √((1-1)^2 + (1-4)^2) = √(0 + 9) = √9 = 3
DF = √((5-1)^2 + (4-1)^2) = √(16 + 9) = √25 = 5
FB = √((8-5)^2 + (7-4)^2) = √(9 + 9) = √18
BC = √((8-8)^2 + (1-7)^2) = √(0 + 36) = √36 = 6
CE = √((8-1)^2 + (1-4)^2) = √(49 + 9) = √58
Perimeter = EA + AD + DF + FB + BC + CE
Perimeter = 5 + 3 + 5 + √18 + 6 + √58 ≈ 25.78 units (since each unit is 100 feet)
Calculate Area:
Area can be calculated using the vertices of the polygon. One method is to use the Shoelace Formula for calculating the area of a polygon with given vertices. The formula is:
Area = 0.5 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|
For the given vertices, the calculations are as follows:
Area = 0.5 * |(17 + 51 + 54 + 81 + 81 + 17) - (45 + 11 + 48 + 78 + 11 + 75)|
Area = 0.5 * |(7 + 5 + 20 + 8 + 8 + 7) - (20 + 1 + 32 + 56 + 1 + 35)|
Area = 0.5 * |55 - 145|
Area = 0.5 * |-90|
Area = 45 square units (since each unit is 100 feet)
So, the perimeter of the lion sanctuary is approximately 25.78 units, and the area is 45 square units.