Question

find the area of the shaded region. round to the nearest tenth if necessary.
13.

1. ( a = )
2. ( a = )

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 40\) in and \(w=15\) in. So, \(A_{rectangle}=40\times15 = 600\) \(in^{2}\).

Step2: Calculate the area of the white - diamond - shaped figure

The white - diamond - shaped figure can be considered as a rhombus. The formula for the area of a rhombus is \(A=\frac{1}{2}\times d_1\times d_2\). Here, assume one diagonal \(d_1 = 40\) in (the length of the rectangle) and \(d_2 = 20\) in. So, \(A_{rhombus}=\frac{1}{2}\times40\times20=400\) \(in^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{rectangle}-A_{rhombus}\). Substitute the values: \(A=600 - 400=200\) \(in^{2}\).

Answer:

\(200\space in^{2}\)