Question

1. find the area of the figure below.

Explanation:

Step1: Divide the figure into a rectangle and a triangle

The rectangle has length from \(x=- 2\) to \(x = 7\) and width from \(y=-7\) to \(y = 2\). The triangle has base from \(x=-2\) to \(x = 7\) and height from \(y = 2\) to \(y=8\).

Step2: Calculate the area of the rectangle

The length of the rectangle \(l=7 - (-2)=9\), and the width \(w = 2-(-7)=9\). The area of a rectangle \(A_{r}=l\times w\), so \(A_{r}=9\times9 = 81\).

Step3: Calculate the area of the triangle

The base of the triangle \(b = 7-(-2)=9\), and the height of the triangle \(h=8 - 2=6\). The area of a triangle \(A_{t}=\frac{1}{2}\times b\times h\), so \(A_{t}=\frac{1}{2}\times9\times6=27\).

Step4: Calculate the total area of the figure

The total area \(A = A_{r}+A_{t}\), so \(A=81 + 27=108\).

Answer:

108