The sides of the rectangular trapezoid are 7 and 25 cm, and the smaller base is 2 cm. Find the area of the trapezium.

Let us denote the trapezoid given by the condition ABCD, BC = 2 cm, AB = 7 cm, CD = 25 cm. From the top of C to the lower base AD, we lower the height CH. Consider a triangle CHD – rectangular, in which the leg CH = AB = 7 cm and the hypotenuse CD = 25 cm are known.Find the unknown leg HD by the Pythagorean theorem:
HD = √ (CD² – CH²) = √ (625 – 49) = √576 = 24 (cm).
Find the lower base AD, AH = BC = 2 cm.
AD = AH + HD = 2 + 24 = 26 (cm).
We find the area of the trapezoid using the formula:
S = 1/2 * (a + b) * h = 1/2 * (BC + AD) * CH = 1/2 * (2 + 26) * 7 = 98 (cm²).
Answer: the area of the trapezoid is 98 cm².