Question

#0
which value is closest to the perimeter of the figure shown on the graph?

a 23 units
b 27.7 units
c 20.7 units
d 13.7 units

Explanation:

Step1: Identify side - lengths

The figure consists of rectangles and a triangle. For the vertical sides of the rectangle part, each has a length of 2 units. For the horizontal sides of the rectangle part, the bottom one has a length of 2 units. For the slanted sides of the triangle, use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. The two slanted sides of the triangle have endpoints: one with endpoints $(0,4)$ and $(2,2)$ and the other with endpoints $(0,4)$ and $(- 2,2)$.

Step2: Calculate slanted - side length

For the slanted side with endpoints $(0,4)$ and $(2,2)$:
\[d=\sqrt{(2 - 0)^2+(2 - 4)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83\]
The other slanted side (with endpoints $(0,4)$ and $(-2,2)$) has the same length $\sqrt{8}\approx2.83$ units.

Step3: Calculate perimeter

The perimeter $P$ of the figure: The vertical sides of the rectangle contribute $2\times2 = 4$ units, the horizontal side of the rectangle contributes 2 units, and the two slanted sides of the triangle contribute $2\times\sqrt{8}\approx5.66$ units. Also, there are two other horizontal segments of length 1 unit each above the rectangle part. So $P=4 + 2+5.66+2\times1=13.66\approx13.7$ units.

Answer:

D. 13.7 units