Question

find the perimeter of the figure below, composed of a rectangle and a semicircle. round to the nearest tenths place. 14 4 answer attempt 2 out of 2 submit answer

Explanation:

Step1: Find length of semicircle arc

The formula for the circumference of a full - circle is $C = 2\pi r$. For a semi - circle, the arc length $l$ is $\frac{1}{2}\times2\pi r=\pi r$. Given $r = 4$, then $l=\pi\times4\approx3.14\times4 = 12.56$.

Step2: Identify lengths of rectangle sides

The rectangle has two lengths of 14 and one width (the side adjacent to the semi - circle) which is equal to the diameter of the semi - circle. The diameter $d = 2r=8$. We only consider one length of the rectangle and the non - adjacent width for the perimeter of the composite figure.

Step3: Calculate perimeter

The perimeter $P$ of the figure is the sum of the semi - circle arc length, one length of the rectangle, and the non - adjacent width of the rectangle. So $P=12.56 + 14+8=34.56$.

Answer:

$34.6$