Answer:
[tex] {\boxed{\sf {269.1 \ square \ units}}} [/tex]
Step-by-step explanation:
To find the area of the figure composed of a rectangle and two semicircles, we'll calculate the area of 2 semicircles and rectangle and add them together.
Area of rectangle is given by,
[tex] {\boxed{\sf{ Area_{(Rectangle)} = length \times width}}}} [/tex]
Here, length of rectangle is 13 and width is 12
Plugging in the values,
[tex] \sf Area_{(Rectangle)} = 13 \times 12[/tex]
[tex] \sf \ \ \ \ \ = 156 \ \ sq. \ units [/tex]
Now, Area of semi circle is given by,
[tex]{\boxed{ \sf{ Area_{(Semicircle)} = \dfrac{\pi r^2}{2} }}}[/tex]
where,
- r is radius of the semicircle
- [tex] \sf \: radius = \dfrac{diameter}{2} = \dfrac{12}{2} = 6 [/tex]
Plugging in the values,
[tex] \sf Area_{(semicircle)}=\dfrac{ 3.14 \times (6)^2 }{2} [/tex]
[tex] \sf \ \ \ \ \ = \dfrac{3.14 \times 36}{2} [/tex]
[tex] \sf \ \ \ \ \ = \dfrac{113.04}{2}[/tex]
[tex] \sf \ \ \ \ \ = 56.52 \: \: sq. \: units [/tex]
The total area is the sum of the rectangle and two semicircles:
[tex]\sf {Total \: Area} = Area_{(rectangle)} + 2 \times Area_{(semicircle)} [/tex]
[tex] \sf {Total \: Area}= 156 + 2 \times 56.52 [/tex]
[tex] \sf {Total \: Area} = 156 + 113.04 [/tex]
[tex] \sf {Total \: Area} = 269.04 [/tex]
Therefore, the area of the figure is 269.1 (near tenth place) square units.
