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Answer :
Final answer:
The perimeter found calculating the length of each side of the polygon and adding them together is 93 units, but there could be a mistake since this option doesn't exist among the choices provided.
Explanation:
The subject of this question is the calculation of the perimeter of a polygon given its vertices' coordinates. The coordinates represent the points in a 2D space. To find the perimeter, you need to calculate the length of each side of the polygon (the distance between each consecutive pair of points), and then add all these lengths together.
To find the perimeter of the shape ABCDEF, we need to calculate the lengths of all the sides and then add them together. Let's label the given points as A(-12,18), B(24,18), C(15,3), D(6,3), E(6,-12), and F(-12,-12). The lengths of the sides AB, BC, CD, DE, EF, and FA can be calculated using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). So, the perimeter is AB + BC + CD + DE + EF + FA. By substituting the coordinates into the formula and calculating each side,Here, points A and B form a horizontal line of length 36 units (the absolute difference of the x-coordinates), B and C, as well as E and F form vertical lines of length 15 units (the absolute difference of the y-coordinates). C, D, E and F form a square of side 9 units (distance between C and D, and E and F).
Therefore, the perimeter is 36 (AB) + 15 (BC) + 9 (CD) + 9 (DE) + 15 (EF) + 9 (FA) which equals 93 units. But since this option doesn't exist in your choices, there's a possibility of a mistake either in the question or in the options provided.
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