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.

Suppose given a rectangular trapezoid ABCD, in which:
angle A = 90 °,
lateral sides – AB = 7 cm, CD = 25 cm,
smaller base – BC = 2 cm.
Let us drop the perpendicular CO from the vertex of the trapezoid C to the side AD.
The area of ​​the trapezoid ABCD will be defined as the sum of the areas of rectangle ABCO and right triangle CDO.
We calculate the area of ​​the rectangle ABCO:
Spr = AB * BC = 7 * 2 = 14 cm ^ 2.
The area of ​​the triangle CDO is:
Str = 1/2 * CO * OD.
CO = AB = 7 cm (as opposite sides of the rectangle ABCO).
Find OD:
OD ^ 2 = CD ^ 2 – CO ^ 2 = 25 ^ 2 – 7 ^ 2 = 625 – 49 = 576;
OD = √576 = 24 cm.
Then
Str = 1/2 * 7 * 24 = 84 cm ^ 2.
Find the area of ​​the trapezoid ABCD:
S = Spr + Spr = 14 + 84 = 98 cm ^ 2.
Answer: 98 cm ^ 2.