Question

determine the perimeter and area of the shape shown below. (both rounded regions are semicircles.) 6 in 6 in perimeter: inches area: square inches

Explanation:

Step1: Calculate curved perimeter

The two semicircles have diameter 6 in. Combined, they form a full circle. Circumference of a circle is $C=\pi d$.
$C = \pi \times 6 = 6\pi$

Step2: Calculate straight perimeter

The shape has two straight sides of 6 in each.
$2 \times 6 = 12$

Step3: Total perimeter

Add curved and straight sections.
$6\pi + 12$

Step4: Calculate square area

Area of the square with side 6 in is $A_{square}=s^2$.
$A_{square} = 6^2 = 36$

Step5: Calculate circle area

The two semicircles form a full circle with radius $r=\frac{6}{2}=3$ in. Area of a circle is $A_{circle}=\pi r^2$.
$A_{circle} = \pi \times 3^2 = 9\pi$

Step6: Total area

Add square and circle areas.
$36 + 9\pi$

Answer:

Perimeter: $6\pi + 12$ (or approximately 30.85 inches)
Area: $9\pi + 36$ (or approximately 64.27 square inches)