Question

find the perimeter of the figure below, composed of a parallelogram and one semicircle. rounded to the nearest tenths place

Explanation:

Step1: Calculate semi - circle arc length

The formula for the circumference of a full circle is $C = 2\pi r$. For a semi - circle, the arc length $l=\pi r$. Given the diameter of the semi - circle is 6, so the radius $r = 3$. Then $l=\pi\times3=3\pi$.

Step2: Calculate lengths of parallelogram sides

The parallelogram has two sides of length 12 and one side of length 6.

Step3: Calculate perimeter

The perimeter $P$ of the figure is the sum of the semi - circle arc length and the non - overlapping sides of the parallelogram. So $P = 3\pi+12 + 12+6$.
$P=3\pi + 30$.
Substitute $\pi\approx3.14$, we get $P\approx3\times3.14 + 30=9.42+30 = 39.42\approx39.4$.

Answer:

$39.4$