Question

What is the area of the polygon?

Answer 1

Hey there!

Let's split this up into four parts as shown by the image here.

Focus on the section to the far left. It is 2 units wide and 5 units long. 
The formula for the area of a triangle is A = 1/2 x l x w.
A = 1/2 x 5 x 2 = 2.5 x 2 = 5 square units is the area of this section.

The second section, the rectangular one, has the dimensions 3 x 5.
The area of this section is 15 square units.

The third section is the one at the top left. It is 4 units wide and 2 units long.
A = 1/2 x 2 x 4 = 1 x 4 = 4 square units is the area of this section.

The last section is the one at the bottom right. It is 4 units wide and 3 units long.
A = 1/2 x 3 x 4 = 1.5 x 4 = 6 square units is the area of this section. 

Now to find the total area of the polygon, which happens to be an irregular pentagon, add up the areas of the sections we divided earlier. 

5 + 15 + 4 + 6 = 30 

The area of this polygon is 30 square units, or 30 u².

Hope this helps!

Answer 2

Look at the picture.
The area of the trapezoid:
$A_1=\dfrac{9+7}{2}\cdot5=\dfrac{16}{2}\cdot5=8\cdot5=40\ \text{units}^2$


The area of the triangle:
$A_2=\dfrac{1}{2}\cdot5\cdot4=\dfrac{1}{2}\cdot20=10\ \text{units}^2$

The area of the polygon:
$A=A_1-A_2\\\\A=40-10=30\ \text{units}^2$