Comparing Area of a Rectangle and a Triangle

Consider two geometric shapes: a rectangle and a triangle.

The rectangle has a length of $10$ units and a width of $6$ units. The area of the rectangle can be calculated using the formula:

$$ ext{Area}_{ ext{rectangle}} = ext{length} imes ext{width}$$

Now consider a triangle that has the same base length as the rectangle's width and a height that is $2$ units shorter than the rectangle's length. Therefore, the base of the triangle is $6$ units, and the height is $10 - 2 = 8$ units. The area of the triangle is given by:

$$ ext{Area}_{ ext{triangle}} =\frac{1}{2} imes ext{base} imes ext{height}$$

Which shape has a greater area?