Question

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

Explanation:

Step1: Calculate rectangle area

The formula for the area of a rectangle is $A_{rect}=l\times w$. Here, $l = 15$ and $w=10$, so $A_{rect}=15\times10 = 150$.

Step2: Calculate area of two - semi - circles (equivalent to one circle)

The two semi - circles together form a full circle. The diameter of the circle $d = 10$, so the radius $r=\frac{d}{2}=5$. The formula for the area of a circle is $A_{circle}=\pi r^{2}$. Substituting $r = 5$ into the formula, we get $A_{circle}=\pi\times5^{2}=25\pi\approx25\times3.14 = 78.5$.

Step3: Calculate total area

The total area of the figure $A=A_{rect}+A_{circle}$. So $A=150 + 78.5=228.5$.

Answer:

$228.5$