Question

answer attempt 1 out of 2 area = units² submit answer

Explanation:

Step1: Divide the shape into simpler shapes

Divide the given polygon into rectangles and triangles.

Step2: Calculate areas of individual shapes

• Rectangle 1: From \(x = - 1\) to \(x = 5\), \(y=-6\) to \(y = 4\). Area \(A_1=(5 - (-1))\times(4-(-6))=6\times10 = 60\).
• Triangle: With base from \(x=-5\) to \(x=-1\) and height from \(y = 0\) to \(y = 2\). Area \(A_2=\frac{1}{2}\times( - 1-(-5))\times2=\frac{1}{2}\times4\times2 = 4\).
• Rectangle 2: From \(x=-5\) to \(x=-1\), \(y=-2\) to \(y = 0\). Area \(A_3=(-1 - (-5))\times2=4\times2 = 8\).

Step3: Sum up the areas

\(A = A_1+A_2+A_3=60 + 4+8=72\).

Answer:

72