Area of the given figure is equal to [tex]86\ cm^{2}[/tex] ( nearest square centimeter).
" Area is defined as the total space occupied by any two-dimensional object enclosed in it."
Formula used
Area of rectangle = length × width
Area of triangle [tex]= \frac{1}{2} \times base \times height[/tex]
Area of semi-circle [tex]= \frac{1}{2} \times (\pi r^{2} )[/tex]
[tex]r=[/tex] radius of the circle
According to the question,
Given figure is composed of :
two congruent rectangles, four congruent triangles, one semi-circle
Given dimensions,
Length of a rectangle [tex]= 6cm[/tex]
Width of a rectangle [tex]= 4cm[/tex]
Height of a triangle [tex]= 4cm[/tex]
Base of a triangle [tex]= 3cm[/tex]
Radius of the semicircle [tex]= \frac{6}{2}[/tex]
[tex]=3cm[/tex]
Substitute the value in the formula to get the required area,
Area of a rectangle [tex]= 6 \times 4[/tex]
[tex]= 24 cm^{2}[/tex]
Area of a triangle [tex]= \frac{1}{2} \times 3\times 4[/tex]
[tex]= 6 cm^{2}[/tex]
Area of a semicircle [tex]= \frac{1}{2} \times \pi \times 3^{2}[/tex]
[tex]=4.5 \times 3.14\\\\= 14.13 cm^{2}[/tex]
Substitute the value to get the required area,
Area of the given composed figure [tex]= 2\times 24 + 4\times 6 + 14.13[/tex]
[tex]= 48 + 24 + 14.13\\\\= 86.13 \ cm^{2}[/tex]
≈ [tex]86 cm^{2}[/tex] (nearest square centimeter)
Hence, Option(B) is the correct answer.
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