9514 1404 393
Answer:
28 square units
Step-by-step explanation:
The figure can be decomposed several ways. Maybe easiest to see is as a 8×4 rectangle with a 2×4 right triangle cut from the corner.
The area of the rectangle is ...
A = LW = (8)(4) = 32
The area of the missing triangle is ...
A = 1/2bh = 1/2(2)(4) = 4
Then the area of the shaded figure is ...
32 - 4 = 28 . . . square units
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<em>Alternate solution</em>
If you divide the figure with a horizontal line across the middle, it becomes a 4×4 square and a trapezoid with bases 2 and 4 and height 4. The shaded area is the sum of these areas.
The area of a trapezoid is ...
A = 1/2(b1 +b2)h
A = (1/2)(2 +4)(4) = 12
The area of the square is ...
A = s² = 4² = 16
Then the total area is ...
12 +16 = 28 . . . square units
