Coordinates (-3,4), (1,4), (-5,2), (1,-4), (5,0). Calculated distances, applied Shoelace Formula. Polygon area: 1/2 |(xy + xy + ... + xy) - (yx + yx + ... + yx)| = 36 sq units.
Given coordinates: (-3, 4), (1, 4), (-5, 2), (1, -4), (5, 0).
Find the distances between consecutive points:
a. Distance between (-3, 4) and (1, 4): d1 = |1 - (-3)| = 4
b. Distance between (1, 4) and (-5, 2): d2 = |-5 - 1| = 6
c. Distance between (-5, 2) and (1, -4): d3 = |1 - (-5)| = 6
d. Distance between (1, -4) and (5, 0): d4 = |5 - 1| = 4
e. Distance between (5, 0) and (-3, 4): d5 = |-3 - 5| = 8
Now, apply the Shoelace Formula to find the area of the polygon:
Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|
Area = 1/2 * |(-3 * 4 + 1 * 2 + (-5) * (-4) + 1 * 0 + 5 * 4) - (4 * 1 + 2 * (-5) + (-4) * 1 + 0 * 5 + 4 * (-3))|
Area = 1/2 * |(-12 + 2 + 20 + 0 + 20) - (4 - 10 - 4 + 0 - 12)|
Area = 1/2 * |50 - (-22)| = 1/2 * 72 = 36 square units