Find the area of pentagon CANDY with vertices C(-6,8), A(3,8), N(6,-2),D(-4,-1),and Y(-7,4).
97.5
97.5
To find the area of pentagon CANDY, we can use the Shoelace Formula. This formula calculates the area of any polygon given the coordinates of its vertices.
The Shoelace Formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) can be found using the following equation:
area = 1/2 * | (x1y2 + x2y3 + ... + xn-1yn + xny1) - (x2y1 + x3y2 + ... + xny(n-1) + x1yn) |
First, let's assign the coordinates of pentagon CANDY:
C = (-6, 8)
A = (3, 8)
N = (6, -2)
D = (-4, -1)
Y = (-7, 4)
Using the coordinates, we can calculate the area of the pentagon. Substituting the values into the Shoelace Formula, we get:
area = 1/2 * | (-6*8 + 3*(-2) + 6*(-1) + (-4)*4 + (-7)*8) - (8*3 + (-2)*(-4) + (-1)*(-7) + 4*(-6) + 8*(-7)) |
Simplifying the equation gives us:
area = 1/2 * | (-48 - 6 - 6 - 16 - 56) - (24 + 8 + 7 - 24 - 56) |
area = 1/2 * | (-132) - (-41) |
area = 1/2 * | (-132 + 41) |
area = 1/2 * | (-91) |
area = 1/2 * 91
area = 45.5
Therefore, the area of pentagon CANDY is 45.5 square units.