The hypotenuse of a right-angled triangle is 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle.

We are given with a right-angled triangle whose measures are
Base $=6m$
Hypotenuse $=6.5m$

Using Pythagoras Theorem:
Hypotenuse${}^2=$ Base${}^2+$ Perpendicular${}^2$
$(6.5{)}^2=(6{)}^2+$ Perpendicular${}^2$
or Perpendicular${}^2=42.25-36=6.25$
or Perpendicular $=2.5m$

Now,
Area of a triangle $=\frac{1}{2}\times Base\times Height$
                              $=\frac{1}{2}\times 6m\times 2.5m$
                              $=7.5c{m}^2$