Answer: area = 30 square units
The diagram is below. Ignore point G and the red dashed line when drawing the final hexagon needed.
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Step-by-step explanation:
On the grid your teacher has given you, plot the 6 points. Then connect them to form hexagon ABCDE. All of this is shown in blue in the diagram below.
Let's add point G as shown in red. I'll connect G to point C with a red dashed line. These will be temporary and erased later. Though if your teacher doesn't mind you leaving it in (so you can show your steps), then its probably not a bad idea to keep it. It's best to ask your teacher.
Anyways, the red segment GC splits the original hexagon into a trapezoid up top and a rectangle down below.
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The trapezoid has the parallel bases of b1 = GC = 4 and b2 = AB = 2. The height is h = GA = 3
This leads to,
area = h*(b1+b2)/2
area = 3*(4+2)/2
area = 3(6)/2
area = 18/2
area = 9
Trapezoid ABCG has area of 9 square units.
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The rectangle has length EF = 7 and width ED = 3
area = length*width
area = 7*3
area = 21
Rectangle DEFG has area of 21 square units.
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Add up those two area results to get the area of the overall hexagon.
trapezoid + rectangle = 9 + 21 = 30 square units.