Given:
The length of the side a is, 11.
The length of the other side b is, a+4 = 11+4 = 15.
The objective is to find the area of trapezium.
The formula to find the area of trapezium is,
[tex]A=\frac{1}{2}h(a+b)[/tex]
Let's find the height of the trapezium using Pythagoras theorem.
[tex]\begin{gathered} \text{Hypotenuse}^2=Opposite^2+Adjacent^2 \\ 5^2=h^2+4^2 \\ h^2=5^2-4^2 \\ h^2=25-16 \\ h^2=9 \\ h=\sqrt[]{9} \\ h=3 \end{gathered}[/tex]
Now, substitute the obtianed values in the formula to find the area of trapezium.
[tex]\begin{gathered} A=\frac{1}{2}\cdot3(11+15) \\ A=\frac{3}{2}(26) \\ A=39 \end{gathered}[/tex]
Hence, the area of trapezium is 39 square units.
