what is the area of the composite figure? (6π + 10) m² (10π + 10) m² (12π + 10) m² (16π + 10) m² 2 m 4 m 5 m

Answer:

A. $(6\pi + 10)\text{ m}^2$

Explanation:

Step1: Calculate area of rectangle

The rectangle has length $l = 5$ m and width $w=2$ m. Area of rectangle $A_{rect}=l\times w=5\times2 = 10$ m².

Step2: Calculate area of semi - ring

Outer radius of semi - ring $R=\frac{4 + 2}{2}=3$ m, inner radius $r = \frac{4}{2}=2$ m. Area of a full ring is $A_{ring}=\pi(R^{2}-r^{2})=\pi(3^{2}-2^{2})=\pi(9 - 4)=5\pi$ m². Area of semi - ring $A_{semi - ring}=\frac{1}{2}\times5\pi=\frac{5\pi}{2}$ m². There are two semi - rings which together form a full ring with area $A_{ring}=5\pi$ m². Also, there is an extra semi - circle with radius $r = 2$ m and area $A_{semi - circle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times2^{2}=2\pi$ m². Net area of circular parts $A_{circular}=5\pi - 2\pi+3\pi$ m².

Step3: Calculate total area

Total area of composite figure $A = A_{rect}+A_{circular}=10 + 6\pi$ m².