Comparing Areas of a Triangle and a Circle

Consider a right triangle XYZ, where angle Z is the right angle. The lengths of sides XY and XZ are 13 units and 12 units respectively. Calculate the area of triangle XYZ, then compare this area to the area of a circle with a radius of 7 units. Which area is greater?

Recall that the area of a right triangle can be calculated using the formula:

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

And the area of a circle is given by:

$$ ext{Area}_{ ext{circle}} = ext{π} imes r^2 $$