Math Problem Solver

The perimeter of a semicircle is $\frac{63}{5} + \frac{63 \pi}{10} \approx 32.39\, \text{units}$.

Note: Approximate solutions are rounded to the nearest hundredths place.

Given: $$\begin{aligned}d&=\frac{63}{5} = 12.6\end{aligned}$$

Perimeter

The perimeter of a semicircle is given by the equation: $$\begin{aligned}P&=\pi r + 2 r\end{aligned}$$ where $P$ is perimeter and $r$ is radius.

Need:$$\begin{aligned}d&=2 r\end{aligned} \quad \Rightarrow \quad \begin{aligned}\frac{63}{5}&=2 r\end{aligned} \quad \Rightarrow \quad \begin{aligned}r&=\frac{63}{10} = 6.3\end{aligned}$$

Solution:$$\begin{aligned}P&=\pi r + 2 r\\P&=\pi \left(\frac{63}{10}\right) + 2 \left(\frac{63}{10}\right)\\P&=\frac{63}{5} + \frac{63 \pi}{10}\end{aligned}$$

A semicircle is a two dimensional figure formed by cutting a circle evenly in half along the diameter d, a line segment passing though the center of the circle. Its radius r is half the diameter, forming a line segment from the center to a point on the circumference.

The circumference C of a semicircle is the measurement of the arc that forms a semicircle, which is half a circle's circumference. $$\begin{aligned} C &= \pi r \\ &= \frac{\pi d}{2} \end{aligned}$$

The perimeter P of a semicircle is the sum of its circumference and diameter. $$\begin{aligned} P &= \pi r + 2 r = r (\pi + 2) \\ &= \pi r + d \end{aligned}$$

The area A of a semicircle is the region enclosed inside it, i.e. half a circle's area. $$A = \frac{\pi r^{2}}{2}$$