Question

find the area of the figure.

Explanation:

Step1: Divide the figure into triangles

We can divide the given polygon into two non - overlapping triangles.

Step2: Recall the area formula for a triangle

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step3: Calculate the area of the first triangle

Let's consider one triangle with vertices that can be used to find base and height easily. Suppose we take a triangle with base along the horizontal and height along the vertical. For the first triangle, assume base $b_1 = 4$ and height $h_1=3$. Then $A_1=\frac{1}{2}\times4\times3 = 6$.

Step4: Calculate the area of the second triangle

For the second triangle, assume base $b_2 = 4$ and height $h_2 = 3$. Then $A_2=\frac{1}{2}\times4\times3=6$.

Step5: Find the total area of the figure

The total area $A = A_1 + A_2$. So $A=6 + 6=12$.

Answer:

12