Find the area of the diagonal section of a regular truncated quadrangular pyramid if its height is √2 cm

Find the area of the diagonal section of a regular truncated quadrangular pyramid if its height is √2 cm, and the sides of the base are 1 cm and 4 cm.

The bases of a regular truncated quadrangular pyramid are squares with sides of 1 cm and 4 cm. The diagonal section is an isosceles trapezoid, the bases of which are equal to the diagonals of the bases of the truncated pyramid, the height is equal to the height of the pyramid.
Knowing the sides of the bases, we can find the diagonals of the bases by the Pythagorean theorem:
d ^ 2 = 1 ^ 2 + 1 ^ 2 = 2;
d = √2;
D ^ 2 = 4 ^ 2 + 4 ^ 2 = 16 * 2;
D = 4√2.
The area of a trapezoid, which is a diagonal section, is found as the product of the half-sum of the bases and the height:
Ssection = h * (D + d) / 2 = √2 * (4√2 + √2) / 2 = √2 * 5√2 / 2 = 5 cm2.