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what is the area of this figure?
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Explanation:

Step1: Divide the figure into simple shapes

Divide the figure into three triangles and one trapezoid.

Step2: Calculate the area of each part

• First triangle (left - upper):

The base \(b_1=(-3)-(-5) = 2\), the height \(h_1 = 5 - 2=3\). Using the formula \(A=\frac{1}{2}bh\), \(A_1=\frac{1}{2}\times2\times3 = 3\).

• Second triangle (middle - upper):

The base \(b_2=1-(-3)=4\), the height \(h_2 = 5 - 2 = 3\). Using the formula \(A=\frac{1}{2}bh\), \(A_2=\frac{1}{2}\times4\times3=6\).

• Third triangle (right - upper):

The base \(b_3=3 - 1=2\), the height \(h_3 = 5 - 2=3\). Using the formula \(A=\frac{1}{2}bh\), \(A_3=\frac{1}{2}\times2\times3 = 3\).

• Trapezoid (lower):

The parallel sides \(a=-1-(-5)=4\) and \(b = 3-(-1)=4\), the height \(h=-1-(-3)=2\). Using the formula \(A=\frac{(a + b)h}{2}\), \(A_4=\frac{(4 + 4)\times2}{2}=8\).

Step3: Sum up the areas of all parts

\(A=A_1+A_2+A_3+A_4\)
\(A=3 + 6+3+8\)

Answer:

\(20\)