Question

answer attempt 2 out of 2 area = units² submit answer

Explanation:

Step1: Divide the shape into rectangles

We can divide the given shape into three rectangles.

Step2: Calculate area of first rectangle

The first rectangle has vertices with length from \(x=- 5\) to \(x = 4\) and height from \(y = 1\) to \(y = 8\). Its length \(l_1=4 - (-5)=9\) and height \(h_1 = 7\), so area \(A_1=l_1\times h_1=9\times7 = 63\).

Step3: Calculate area of second rectangle

The second rectangle has vertices with length from \(x = 1\) to \(x = 4\) and height from \(y = 1\) to \(y = 3\). Its length \(l_2=4 - 1=3\) and height \(h_2=2\), so area \(A_2=l_2\times h_2=3\times2 = 6\).

Step4: Calculate area of third rectangle

The third rectangle has vertices with length from \(x=-5\) to \(x = 4\) and height from \(y=-2\) to \(y = 1\). Its length \(l_3=4-(-5)=9\) and height \(h_3 = 3\), so area \(A_3=l_3\times h_3=9\times3=27\).

Step5: Sum up the areas

The total area \(A = A_1+A_2+A_3=63 + 6+27=96\).

Answer:

96