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Use the quadrant system to find the area of the polygon shown

44 square units
54 square units
36 square units
52 square units

Use the quadrant system to find the area of the polygon shown 44 square units 54 square-example-1

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3 votes

use the quadrant system to find the area of the polygon shown

44 square units

54 square units

36 square units

52 square units

True 44 square units

User Stanislav Levental
by
8.4k points
4 votes

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

User Dan Friedman
by
8.1k points

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