Applications of definite integral

Find the missing real positive constant $a$ so that the area of the yellow triangle indicated in the picture is $12$ square units.

Which of the following formulas does NOT express the area of the yellow triangle indicated in the picture?

Peter and Jane both calculated the volume of a solid of revolution using a definite integral. Both chose a solid obtained by rotation of a line segment about the $x$-axis. The endpoints of Peter’s line segment are $[0;1]$ and $[5;4]$, the endpoints of Jane’s line segment are $[0;3]$ and $[5;0]$. Finally, they compared their calculated volumes. Which of the following statements is true?

A right trapezoid is bounded by $y=ax+1$, $x=0$, $x=6$, and by the $x$-axis. Rotating the trapezoid around the $x$-axis we get a truncated cone. Find the value of the parameter $a>0$ so that the volume of the truncated cone is $26\pi$.