Question

12 cm
25 cm
perimeter =
area =

Explanation:

Step1: Calculate the perimeter of the semi - circle

The diameter of the semi - circle is 12 cm, so the radius $r = 6$ cm. The formula for the circumference of a full - circle is $C = 2\pi r$, and for a semi - circle is $C_{semicircle}=\pi r$. So $C_{semicircle}=\pi\times6 = 6\pi$ cm.

Step2: Calculate the lengths of the straight parts of the figure

The two straight parts of the figure are two lengths of 25 cm and one width of 12 cm. The sum of the lengths of the straight parts is $2\times25+12=50 + 12=62$ cm.

Step3: Calculate the perimeter of the whole figure

The perimeter $P$ of the figure is the sum of the length of the semi - circle and the lengths of the straight parts. So $P=6\pi+62$. Taking $\pi\approx3.14$, we have $P = 6\times3.14+62=18.84 + 62=80.84$ cm.

Step4: Calculate the area of the rectangle

The area of the rectangle part is $A_{rectangle}=25\times12 = 300$ $cm^{2}$.

Step5: Calculate the area of the semi - circle

The formula for the area of a full - circle is $A=\pi r^{2}$, and for a semi - circle is $A_{semicircle}=\frac{1}{2}\pi r^{2}$. With $r = 6$ cm, $A_{semicircle}=\frac{1}{2}\pi\times6^{2}=\frac{1}{2}\pi\times36 = 18\pi$ $cm^{2}$. Taking $\pi\approx3.14$, $A_{semicircle}=18\times3.14 = 56.52$ $cm^{2}$.

Step6: Calculate the area of the whole figure

The area $A$ of the figure is the sum of the area of the rectangle and the area of the semi - circle. So $A=300 + 18\pi\approx300+56.52=356.52$ $cm^{2}$.

Answer:

Perimeter: $80.84$ cm
Area: $356.52$ $cm^{2}$