Find the area of an isosceles trapezoid if its smaller base is 7 cm, the lateral side is 10 cm, and the height is 8.

We will start from the fact that the trapezoid in the problem is isosceles.
Let us draw the height from the upper left point of the vertex to the lower base and the point of intersection of the base and the height will be called P.
Let’s draw one more such height from the right extreme point of the upper base. It will cross the bottom base at point O.
Let the lower base AD, the upper one BC.
We have two triangles ABP and OСD.
Let’s find their legs, which will be the same, lying on AD:
AP = OD = √ (10² – 8²) = √ (100 – 64) = √36 = 6 (cm).
Find the lower base of AD:
6 * 2 + 7 = 12 + 7 = 19 (cm).
Find the area of ​​the trapezoid:
(7 + 15): 2 * 8 = 22: 2 * 8 = 11 * 8 = 88 (cm²).
ANSWER: the area is 88 cm².