### Example 2: Analyzing a Composite Area**Problem Statement:**Consider the shaded area shown in Figure 1. Suppose that \( a = 140 \, \text{mm} \), \( b = 200 \, \text{mm} \), and \( r = 80 \, \text{mm} \).**Diagram Explanation:**The figure depicts a composite shape consisting of a larger trapezoidal section with a circular cutout:- **Trapezoid Details:** - The trapezoid has a base width along the \( x \)-axis comprised of two segments, each labeled \( a \) and \( b \). These distances suggest that the entire base length is \( a + b = 340 \, \text{mm} \). - The height from the \( x \)-axis to the top parallel side is \( 2b = 400 \, \text{mm} \).- **Circular Cutout:** - A circle with radius \( r = 80 \, \text{mm} \) is subtracted from the trapezoidal area. The circle is centered at a position within the trapezoid.This diagram assists in understanding how composite geometric areas are calculated by combining simpler shapes and subtracting intersections or voids. **Problem Statement:**Determine the moment of inertia of the shaded area about the \( y \) axis.**Instructions:**Express your answer to three significant figures and include the appropriate units.**Input Section:**- \( I_y = \) [Value] [Units]**Note:** There are also interactive elements such as buttons for grid view and formatting, but they are not the focus here.

Name: ### Example 2: Analyzing a Composite Area**Problem Statement:**Consid
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: ### Example 2: Analyzing a Composite Area**Problem Statement:**Consider the shaded area shown in Figure 1. Suppose that \( a = 140 \, \text{mm} \), \( b = 200 \, \text{mm} \), and \( r = 80 \, \text{mm} \).**Diagram Explanation:**The figure depicts

Givena=140mmb=200mmr=80mmthe inertia about y axisIy=2b2a33-πr44+πr2a2+2bb336+122b×b×2a+b32Iy=400×28033-π×8044+π×802×1402+400×200336+12×400×200×280+20032Iy=2926.933×106-426.251×106+4896×106Iy=7396.682×106 mm4