Answer: 24
Explanation:
To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.
Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.
The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.
Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19
Radius of the circle = 4.19/60 = 0.07
Angle of sector = 360 - 60 = 300 degrees
Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041
The area of the triangle can be found using the formula:
Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24
Therefore, the total area of the composite figure is:
0.0041 + 24 = 24.0041
Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.