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

A trapezoid is a quadrilateral in which two sides are parallel and the other two are not parallel.
A rectangular trapezoid is called, in which one side is perpendicular to the base.
The area of ​​the trapezoid is calculated using the following formula:
S = (a + b) / 2 ∙ h, where:
S is the area of ​​the trapezoid;
a – smaller base;
b – larger base;
h is the height of the trapezoid;
In order to find the area of ​​a trapezoid, you need to calculate the length of its larger base. Since the distance between the heights in the trapezoid is equal to the length of the smaller base AH = BC, then AD = AH + HD.
To calculate the segment НD, consider the triangle ΔСDН. This triangle is rectangular.
To calculate the length НD, we use the Pythagorean theorem, according to which, the square of the hypotenuse is equal to the sum of the squares of the legs:
CD ^ 2 = CH ^ 2 + HD ^ 2;
НD ^ 2 = СD ^ 2 – CH ^ 2;
CH = AB = 7 cm.
НD ^ 2 = 25 ^ 2 – 7 ^ 2 = 625 – 49 = 576;
НD = √576 = 24;
AD = 24 + 2 = 26 cm.
S = (2 + 26) / 2 7 = 28/2 ∙ 7 = 98 cm2.
Answer: the area of ​​the trapezoid is 98 cm2.