I’ll give the Brainliest to who answers this question with a reasonable explanation. Find the area of the figure below. Show all your work.

Thank you.

Step-by-step explanation:

The composite figure shown in the picture consists of a semi-circle and a trapezoid. We can even break this trapezoid into a rectangle and two triangles for even simpler calculations. We can find the total area of the figure by simply adding the total area of the shapes we will break the figure into:

Area of semi-circle (half the area of a circle):

Area of trapezoid (average of bases multiplied by height):

Thus, the total area of the figure is:

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this