Find the area of the parallelogram with vertices A(3, 0), B(1, 4), C(6, 3), and D(4, 1)

To find the area of a parallelogram given its vertices, we can use the determinant method based on the coordinates of the vertices. The area can be calculated using the formula:

Area = | (x_Ay_B + x_By_C + x_Cy_D + x_Dy_A) – (y_Ax_B + y_Bx_C + y_Cx_D + y_Dx_A) | / 2

Substituting the given coordinates:

• A(3, 0) ⇒ x_A = 3, y_A = 0
• B(1, 4) ⇒ x_B = 1, y_B = 4
• C(6, 3) ⇒ x_C = 6, y_C = 3
• D(4, 1) ⇒ x_D = 4, y_D = 1

Plugging in these values:

Area = | (3*4 + 1*3 + 6*1 + 4*0) – (0*1 + 4*6 + 3*4 + 1*3) | / 2

Calculating each term gives us:

• 3*4 = 12
• 1*3 = 3
• 6*1 = 6
• 4*0 = 0
• 0*1 = 0
• 4*6 = 24
• 3*4 = 12
• 1*3 = 3

So we can rewrite the area expression as:

Area = | (12 + 3 + 6 + 0) – (0 + 24 + 12 + 3) | / 2

This simplifies to:

Area = | 21 – 39 | / 2 = | -18 | / 2 = 18 / 2 = 9

Therefore, the area of the parallelogram is 9 square units.