find the area of the following shape. you must show all work to receive credit.

12 square units

step-by-step explanation:

method 1:

break up the area into well known shapes such as triangles, rectangles and trapezoids. then find the area of each one and add them together.

draw a segment from point (-2, 2) to point (1, 2).

above that you have a triangle. the base is 4 units. the height is 2 units.

area of triangle = base * height/2

area of triangle = 4 * 2/2 = 4 square units

below the segment we drew, there s a trapezoid.

area of trapezoid = (1/2)(large base + small base)(height)

the large base measures 5 units. the small base measures 3 units. the height is 2 units.

area of trapezoid = (1/2)(5 + 3)(2) = 8 square units

total area = area of triangle + area of trapezoid =

= 4 square units + 8 square units = 12 square units

method 2:

the figure is made up of squares and triangles from the grid. each square in the grid has an area of 1 square units. because of the slopes of the inclined sides, each triangle has an area of 1/2 square unit.

add up all full grid squares in the figure: 9

add up all grid triangles in the figure: 6 grid triangles

area = area of grid square + area of grid triangles

area = 9 square units + 6 * (1/2) square units

area = 9 square units + 3 square units

area = 12 square unis

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

the correct answer is x/3+10≥32

hope this !