Question

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1. find the area of this shape. show your reasoning.

Explanation:

Step1: Enclose the shape in a rectangle

Assume each square has side - length 1. Enclose the given shape in a rectangle of length 9 and width 5. The area of the rectangle $A_{rect}=9\times5 = 45$.

Step2: Calculate the area of non - shaded triangles

There are 3 non - shaded right - angled triangles.
The first triangle on the left has base 4 and height 3, so its area $A_1=\frac{1}{2}\times4\times3=6$.
The second triangle in the middle has base 3 and height 2, so its area $A_2=\frac{1}{2}\times3\times2 = 3$.
The third triangle on the right has base 4 and height 3, so its area $A_3=\frac{1}{2}\times4\times3=6$.

Step3: Calculate the area of the shaded shape

The area of the shaded shape $A = A_{rect}-A_1 - A_2 - A_3$.
$A=45-(6 + 3+6)=45 - 15=30$.

Answer:

30