Question

To the nearest tenth, What is the area of a shaded segment when AG= 6 ft

Answer 1

Answer:

28.3 square feet

Explanations:

The formula for calculating the area of the shaded segment is expressed as:

$A=\frac{1}{2}\times r^2(\theta-sin\theta)$

where:

r is the radius = AG = 6ft

θ = 90 degrees

Substitute the given parameter into the formula

$\begin{gathered} A=\frac{1}{2}\times6^2(\frac{\pi}{2}-sin(\frac{\pi}{2})) \\ A=\frac{1}{2}\times36(\frac{\pi}{2}-1) \\ A=18(\frac{\pi}{2}-1) \\ \end{gathered}$

Since π = 3.14, then;

$\begin{gathered} A=18(\frac{3.14}{2}-1) \\ A=18(1.57-1) \\ A=18(0.57) \\ A=28.26 \\ A\approx28.3ft^2 \end{gathered}$

Hence the area of the shaded region is 28.3 square feet