What is the area of the composite figure whose vertices have the following coordinates? (−2, −2) , (4, −2) , (5, 1) , (2, 3) , (−1, 1) Enter your answer in the box. units²
Accepted Solution
A:
Answer:24 square unitsStep-by-step explanation:Try this method. First write the coordinates of each point on a new line. Repeat the first point at the bottom after the dashed line. -2 -2 4 -2 5 1 2 3 -1 1 ---------- -2 -2Now multiply each x-coordinate from the left column by the y-coordinate below it in the right column and write the answer to the right. I did it below in bold. -2 -2 4 -2 4 5 1 4 2 3 15 -1 1 2 ---------- -2 -2 2Now multiply each y-coordinate from the right column by the x-coordinate below it in the left column and write the answer to the left. I did it below in bold. -2 -2 -8 4 -2 4 -10 5 1 4 2 2 3 15 -3 -1 1 2 ---------- -2 -2 -2 2Add the numbers in the left bold column and add the number in the right bold column. -2 -2 -8 4 -2 4 -10 5 1 4 2 2 3 15 -3 -1 1 2 ---------- -2 -2 -2 2---------------------------------21 27The area of the polygon is the absolute value of half of the right sum minus the left sum.A = | 1/2 (right sum - left sum) |A = | 1/2 (27 - (-21) |A = | 1/2(48) |A = |24|A = 24Area = 24 square units