Question

find the area of the figure below, composed of a rectangle and a semicircle. round to the nearest tenths place.

Explanation:

Step1: Calculate rectangle area

The formula for the area of a rectangle is $A_{rect}=l\times w$, where $l = 7$ and $w = 4$. So $A_{rect}=7\times4 = 28$.

Step2: Calculate semicircle area

The diameter of the semicircle is 4, so the radius $r=\frac{4}{2}=2$. The formula for the area of a full - circle is $A_{circle}=\pi r^{2}$, and for a semicircle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = 2$ into the formula, we get $A_{semicircle}=\frac{1}{2}\pi\times2^{2}=2\pi\approx2\times3.14 = 6.28$.

Step3: Calculate total area

The total area $A = A_{rect}+A_{semicircle}=28 + 6.28=34.28\approx34.3$.

Answer:

$34.3$