What is the best approximation for the area of this figure?

This area can be seen as a semicircle plus a triangle. So, we will find the area of each figure and then add both to get the total area.

The area of a triangle is given by the following formula:

  (1)

Where is the base and   is the height.

  (2)

Now we are going to find the area of the cemicircle, which is the half of the area of a circle:

  (3)

Where is the radius, in order to find it we have to calculate the diameter of this semicircle first, and we will do it as follows:

We know the points of the ends of the diameter, which are:

and

We have to use the Pithagorean theorem to calculate the distance between both points (taking into account the x-component and the y-component of each one)

>>>>This is the diameter of the semicircle

Then, the radius is:

Now we can use the formula written in equation (3):

  (4)

Adding (2) and (4):

>>>>This is the answer