Question

find the area of this shape. show your reasoning.

Explanation:

Step1: Identify the shape components

The shaded shape can be divided into two triangles. Let's assume the base of each triangle is \( b \) and the heights are \( h_1 \) and \( h_2 \). From the grid, we can observe that the total height (sum of \( h_1 \) and \( h_2 \)) is 6 units, and the base length is 4 units.

Step2: Use the triangle area formula

The area of a triangle is \( A=\frac{1}{2} \times \text{base} \times \text{height} \). For the two triangles combined, since they share the same base, the total area \( A \) is \( \frac{1}{2} \times \text{base} \times (h_1 + h_2) \).

Step3: Substitute the values

Here, base \( = 4 \) and \( h_1 + h_2=6 \). So, \( A=\frac{1}{2} \times 4\times 6 \).

Step4: Calculate the result

\( \frac{1}{2} \times 4\times 6 = 2\times 6 = 12 \).

Answer:

The area of the shape is \( 12 \) square units.