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

good bye

step-by-step explanation:

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