Questions: Find the perimeter of the shape.

Solution Steps

The coordinates of the vertices are A(-4, 3), B(0, 2), C(2, 4), and D(0, -3).

We use the distance formula to find the length of each side: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

AB = \(\sqrt{(-4 - 0)^2 + (3 - 2)^2} = \sqrt{16 + 1} = \sqrt{17}\) BC = \(\sqrt{(2 - 0)^2 + (4 - 2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}\) CD = \(\sqrt{(2 - 0)^2 + (4 - (-3))^2} = \sqrt{4 + 49} = \sqrt{53}\) DA = \(\sqrt{(-4 - 0)^2 + (3 - (-3))^2} = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13}\)

Perimeter = AB + BC + CD + DA Perimeter = \(\sqrt{17} + 2\sqrt{2} + \sqrt{53} + 2\sqrt{13}\) Perimeter ≈ 4.12 + 2.83 + 7.28 + 7.21 Perimeter ≈ 21.44

Final Answer