Area of the given figure is equal to \(86\ cm^{2}\) ( nearest square centimeter).
What is area?
" 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 \(= \frac{1}{2} \times base \times height\)
Area of semi-circle \(= \frac{1}{2} \times (\pi r^{2} )\)
\(r=\) 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 \(= 6cm\)
Width of a rectangle \(= 4cm\)
Height of a triangle \(= 4cm\)
Base of a triangle \(= 3cm\)
Radius of the semicircle \(= \frac{6}{2}\)
\(=3cm\)
Substitute the value in the formula to get the required area,
Area of a rectangle \(= 6 \times 4\)
\(= 24 cm^{2}\)
Area of a triangle \(= \frac{1}{2} \times 3\times 4\)
\(= 6 cm^{2}\)
Area of a semicircle \(= \frac{1}{2} \times \pi \times 3^{2}\)
\(=4.5 \times 3.14\\\\= 14.13 cm^{2}\)
Substitute the value to get the required area,
Area of the given composed figure \(= 2\times 24 + 4\times 6 + 14.13\)
\(= 48 + 24 + 14.13\\\\= 86.13 \ cm^{2}\)
≈ \(86 cm^{2}\) (nearest square centimeter)
Hence, Option(B) is the correct answer.
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