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  

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!