# The length of a circle inscribed in a rectangular trapezoid is 24π cm. Calculate the area of the trapezoid

**The length of a circle inscribed in a rectangular trapezoid is 24π cm. Calculate the area of the trapezoid if its lower base is 10 cm larger than the upper one.**

We have a trapezoid ABCD, where AB, CD are the sides, BC, AD are the bases. If a circle can be inscribed in a quadrilateral, then AB + CD = BC + AD, based on the fact that the length of the circle is 24π, then the radius is 12, then the side AB is 24 cm.Let us draw the height CK, then KD = 10 cm, the length of the height is equal to the length AB and is equal to 24 cm, according to the Pythagorean theorem, we find the hypotenuse CD from the right-angled triangle CKD: (10 ^ 2 + 24 ^ 2) ^ 1/2 = 26 cm, let BC – x, AD – (x + 10):

x + x + 10 = 24 + 26

x = 20

Then the area is equal to:

S: ((20 + 30) / 2) * 24 = 600