Question

in simplest form, find the area of the shaded portion of the figure below if ( x = 4 ), ( y = 1.9 ), ( w = 3.3 ), and ( z = 4 ). all figures are in inches; round to the nearest tenth.

area_figure =
_____ in²

Explanation:

Step1: Calculate the area of the rectangle with sides \(x\) and \(y\)

The area of a rectangle is \(A = length\times width\). For the rectangle with sides \(x = 4\) and \(y=1.9\), its area \(A_1=4\times1.9 = 7.6\)

Step2: Calculate the area of the triangle in the first rectangle

The area of a triangle is \(A=\frac{1}{2}\times base\times height\). Assume the base and height of the triangle in the first rectangle are \(x = 4\) and \(y = 1.9\) (by visual inspection of the figure). The area of the triangle \(A_{t1}=\frac{1}{2}\times4\times1.9=3.8\)

Step3: Calculate the area of the un - shaded part of the first rectangle

The un - shaded part of the first rectangle \(A_{u1}=A_1 - A_{t1}=7.6-3.8 = 3.8\)

Step4: Calculate the area of the second rectangle

The area of the second rectangle with sides \(w = 3.3\) and \(z = 4\) is \(A_2=3.3\times4=13.2\)

Step5: Calculate the total area of the shaded part

The total area of the shaded part \(A=A_{u1}+A_2\)
Substitute \(A_{u1}=3.8\) and \(A_2 = 13.2\) into the formula: \(A=3.8 + 13.2=17\)

Answer:

\(17.0\)