Question

find the perimeter of the following shape, rounded to the nearest tenth. image of a grid with a diamond - shaped figure and multiple - choice options: 8, 11.3, 12, 17.9

Explanation:

Step1: Identify the shape and side lengths

The shape is a rhombus (all sides equal). To find the length of one side, use the distance formula between two adjacent vertices. Let's take vertices \( A(2, 3) \) and \( D(0, 5) \) (assuming coordinates from the grid). The distance formula is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
For \( A(2, 3) \) and \( D(0, 5) \): \( x_1 = 2, y_1 = 3, x_2 = 0, y_2 = 5 \)
\( d = \sqrt{(0 - 2)^2 + (5 - 3)^2} = \sqrt{(-2)^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.828 \)

Step2: Calculate the perimeter

Since a rhombus has 4 equal sides, perimeter \( P = 4 \times \) side length.
\( P = 4 \times \sqrt{8} \approx 4 \times 2.828 \approx 11.312 \approx 11.3 \) (rounded to the nearest tenth)

Answer:

11.3