We are given the following information about a trapezoid.
Area = 46 sq cm
Height = 4 cm
Longer base = 15 cm
We are asked to find the shorter base of the trapezoid.
Recall that the area of a trapezoid is given by
[tex]A=\frac{a+b}{2}\cdot h[/tex]
Let us substitute the given values and solve for the shorter side of the trapezoid.
[tex]\begin{gathered} 46=(\frac{a+15}{2})\cdot4 \\ 2\cdot46=(a+15)\cdot4 \\ 92=(a+15)\cdot4 \\ \frac{92}{4}=a+15 \\ 23=a+15 \\ a=23-15 \\ a=8\; cm \end{gathered}[/tex]
Therefore, the shorter base of the trapezoid is 8 cm
