Question

find the area of the shapes above the x - axis.
o 30 + 2π²
o 21 + 4π
o 21 + 2π
o 21 + 2π²
o 30 + 2π

Explanation:

Step1: Analyze the shapes

The figure consists of a semi - circle and a trapezoid.

Step2: Calculate the area of the semi - circle

The radius of the semi - circle $r = 2$. The area of a full - circle is $A_{circle}=\pi r^{2}=\pi\times2^{2}=4\pi$, so the area of the semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times4 = 2\pi$.

Step3: Calculate the area of the trapezoid

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a = 3$, $b = 7$, and $h = 6$. So $A_{trapezoid}=\frac{(3 + 7)\times6}{2}=30$.

Step4: Calculate the total area

The total area $A = A_{trapezoid}+A_{semicircle}=30 + 2\pi$.

Answer:

$30 + 2\pi$