Question

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

Answer 1

28.3 square feet

Explanations:

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

`A=(1)/(2)* 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=(1)/(2)*6^2((\pi)/(2)-sin((\pi)/(2))) \\ A=(1)/(2)*36((\pi)/(2)-1) \\ A=18((\pi)/(2)-1) \\ \end{gathered}`

Since π = 3.14, then;

`\begin{gathered} A=18((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