Question

the figure below shows a semicircle joined to a rectangle with distances given in units. what is the area, in square units, of this figure? f. 22 + 5pi g. 24 + 6pi h. 24 + 2pi j. 24 + 4pi k. 24 + 8pi

Explanation:

Step1: Calculate rectangle area

The length of the rectangle is $2 + 4+ 2=8$ units and the width is 3 units. The area formula for a rectangle is $A = lw$. So, $A_{rectangle}=8\times3 = 24$ square - units.

Step2: Calculate semi - circle area

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

Step3: Calculate total area

The total area of the figure $A = A_{rectangle}+A_{semicircle}$. So, $A = 24 + 2\pi$.

Answer:

H. $24 + 2\pi$