What is the AREA of the following shape A propeller blade sp

What is the AREA of the following shape? A propeller blade spinning at 4500 rpm has blades that are 3.00 feet long, fast (in ft/s) are the tips of the blades moving through the air? If Bob pulls the heavy crate SOUTH with a force of 5.00 N and Grace pulls the heavy crate WEST with a force of 12.0 N. what is the magnitude and direction of the resulting Force? Express the answer in either Compass or Polar notation.

Solution

the figure has a sector of circle and a quadrilateral

area of sector of circle is given by

A = r^2 theta / 2

theta = 60 degrees

r = 6.2

A = 60/360 ( 3.14 (6.2)^2 )

A = 20.117 square feet

now finding area of trapezoid ( rectangle - right angled triangle )

height of trapezoid is

h^2 = (6.2)^2 - (6.2-3.1)^2

h = 5.37 feet

area of rectangle = 3.1 * 5.37 = 16.645

area of right angle triangle = 1/2 * 5.37 * 3.1 = 8.3235

hence area of figure = area of sector + area of rectangle - area of right angle triangle

= 20.117 + 16.645 - 8.3235

Area of figure = 28.4385 sq feet