Given:
Area of trapezoid = 6096 square centimeters
Shorter base = 23 centimeters
Longer base = 65 centimeters
Let's find the height of the trapezoid.
To find the height, apply the formula:
[tex]A=\frac{a+b}{2}*h[/tex]Where:
A is the area = 6096 square centimeters
a is the shorter base = 23 centimeters
b is the longer base = 65 centimeters.
Let's find the height.
Rewrite the formula for h:
[tex]h=\frac{2A}{a+b}[/tex]Substitute values into the formula and solve for h:
[tex]\begin{gathered} h=\frac{2*6096}{23+65} \\ \\ h=\frac{12192}{88} \\ \\ h=138.5\text{ cm} \end{gathered}[/tex]Therefore, the height of the trapezoid is 138.5 centimters.
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