Question

find the perimeter of the following shape rounded to the nearest tenth

Explanation:

Step1: Identify side - length using grid

Assume each grid square has side - length 1. Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ to find the length of each side of the diamond - shaped figure. If we consider the right - triangles formed by the grid lines for each side of the diamond, for example, for one side, the legs of the right - triangle are 2 and 2. Then $c=\sqrt{2^{2}+2^{2}}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$.

Step2: Calculate perimeter

The diamond has 4 equal sides. The perimeter $P = 4c$. Substituting $c = 2\sqrt{2}$, we get $P=4\times2\sqrt{2}=8\sqrt{2}\approx8\times1.414 = 11.312$.

Step3: Round to nearest tenth

Rounding 11.312 to the nearest tenth gives 11.3.

Answer:

11.3