# Find the area of a rectangular trapezoid, the sides are 15 and 17 cm, and the smaller base is 12.

The smaller side of a rectangular trapezoid is perpendicular to the bases, which means it is equal to the height of the trapezoid. Consider a right-angled triangle, in which the hypotenuse is the large side of the trapezium, the legs are the height of the trapezium and the projection of the larger side to the larger base. The sum of the squares of the legs is equal to the square of the hypotenuse, we can find the unknown leg:

17 ^ 2-15 ^ 2 = 289-225 = 64;

The side projection is √64 = 8 cm.

The larger base of the trapezoid is equal to the sum of the lengths of the smaller base and the projection of the larger lateral side onto the larger base: 12 + 8 = 20 cm.

The area of the trapezoid is equal to the product of the half-sum of the bases and the height: S = 15 * (12 + 20) / 2 = 15 * 16 = 240 cm2.