Question

Please help!!

Answer 1

Answer: area = 30 square units

The diagram is below. Ignore point G and the red dashed line when drawing the final hexagon needed.

======================================================

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.

------------

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.

-----------

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.

------------

Add up those two area results to get the area of the overall hexagon.

trapezoid + rectangle = 9 + 21 = 30 square units.