Question

find the perimeter of the figure below, composed of an isosceles trapezoid and one semi - circle. rounded to the nearest tenths place

Explanation:

Step1: Find length of semi - circle arc

The formula for the circumference of a full circle is $C = \pi d$. For a semi - circle, the arc length $l$ with diameter $d = 8$ is $l=\frac{1}{2}\pi d$. So, $l=\frac{1}{2}\times\pi\times8 = 4\pi$.

Step2: Sum up the lengths of trapezoid sides

The trapezoid has two non - parallel sides of length 10 and one parallel side of length 14. We don't include the bottom parallel side of length 8 (as it is replaced by the semi - circle). The sum of the trapezoid sides is $10 + 10+14=34$.

Step3: Calculate the perimeter

The perimeter $P$ of the figure is the sum of the semi - circle arc length and the lengths of the trapezoid sides. So, $P = 34+4\pi$.
Using $\pi\approx3.14$, we have $P=34 + 4\times3.14=34+12.56 = 46.56\approx46.6$.

Answer:

$46.6$