For this case we have a figure composed of a trapezoid and a triangle.
By definition we have that the area of a trapezoid is given by:
[tex]A = \frac {(B + b) * h} {2}[/tex]
Where:
B: It's the biggest side
b: It is the minor side
h: It's the height.
So:
[tex]A = \frac {(14 + 4) * 10} {2}\\A = 90 \ cm ^ 2[/tex]
For its part, the area of a triangle is:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b: It's the base
h: It's the height
[tex]A = \frac {14 * (18-10)} {2}\\A = \frac {14 * 8} {2}\\A = \frac {14 * 8} {2}\\A = 56 \ cm ^ 2[/tex]
Thus, the total area is the sum of the two areas:
[tex]146 \ cm ^ 2[/tex]
ANswer:
[tex]146 \ cm ^ 2[/tex]
