Question

question 5(multiple choice worth 1 points) (04.03 mc) find the perimeter of the following shape, rounded to the nearest tenth options: 8, 11.3, 12, 17.9

Explanation:

Step1: Identify the shape and side lengths

The shape is a rhombus (or a diamond - shaped figure) on a coordinate grid. To find the length of each side, we can use the distance formula between two points. Let's consider the coordinates of the vertices. For example, if we take two adjacent vertices, say from (0, 2) to (2, 0), the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1=2,x_2 = 2,y_2 = 0\). So \(d=\sqrt{(2 - 0)^2+(0 - 2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.828\).

Step2: Calculate the perimeter

Since a rhombus has 4 equal - length sides, the perimeter \(P\) is \(4\times\) side length. So \(P = 4\times2\sqrt{2}=8\sqrt{2}\approx8\times1.414 = 11.312\approx11.3\) (rounded to the nearest tenth).

Answer:

11.3