Estimate the area of the land to the nearest square meter

To estimate the area of the land, we will use the coordinates of the vertices determined in the previous step and apply the Shoelace Formula (also known as Gauss's Area Formula). Step 1: List the coordinates of the vertices in order. Let point A be the origin (0,0). • A = (0,0) • Q = (16, -8) • P = (44, -16) • B = (56, 0) • S = (26, 32) • R = (16, 18) Step 2: Apply the Shoelace Formula. The formula for the area of a polygon with vertices (x_1, y_1), (x_2, y_2), , (x_n, y_n) is: Area = (1)/(2) | (x_1y_2 + x_2y_3 + + x_ny_1) - (y_1x_2 + y_2x_3 + + y_nx_1) | We list the coordinates and repeat the first point at the end: (x_1, y_1) = (0, 0) (x_2, y_2) = (16, -8) (x_3, y_3) = (44, -16) (x_4, y_4) = (56, 0) (x_5, y_5) = (26, 32) (x_6, y_6) = (16, 18) (x_7, y_7) = (0, 0) (repeat of the first point) Step 3: Calculate the sum of the products (x_i y_i+1). (0 × -8) + (16 × -16) + (44 × 0) + (56 × 32) + (26 × 18) + (16 × 0) = 0 - 256 + 0 + 1792 + 468 + 0 = 2004 Step 4: Calculate the sum of the products (y_i x_i+1). (0 × 16) + (-8 × 44) + (-16 × 56) + (0 × 26) + (32 × 16) + (18 × 0) = 0 - 352 - 896 + 0 + 512 + 0 = -736 Step 5: Substitute the sums into the Shoelace Formula and calculate the area. Area = (1)/(2) | 2004 - (-736) | Area = (1)/(2) | 2004 + 736 | Area = (1)/(2) | 2740 | Area = 1370 The area of the land is 1370 square meters. Since the question asks to estimate to the nearest square meter, the answer is already in the correct format. The estimated area of the land is 1370 square meters. Last free one today — make it count tomorrow, or type /upgrade for unlimited.