Answer and Step-by-step explanation:
Use the Pythagorean Theorem to solve for the height.
[tex]a^{2}+ b^{2}= c^{2} \\\\\\4^{2} + b^{2} = 5^{2}\\\\\\16 + b^{2} = 25\\\\\\b^{2} = 9\\\\\\b = 3[/tex]
The height of the triangle is 3.
Now we can solve the shapes in the trapezoid.
4 times 3 = 12 (Rectangle)
[tex]\frac{4 * 3}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6 (Triangle)
12 + 6 = 18 (Trapezoid)
The area of the trapezoid is 18 [tex]units^{2}[/tex].
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