In an isosceles trapezoid, the bases are 8 cm and 16 cm. The diagonals intersect at right angles.

In an isosceles trapezoid, the bases are 8 cm and 16 cm. The diagonals intersect at right angles. Find the height of the trapezoid.

Let’s draw the height of the trapezoid KH through the center of intersection of the diagonals.

In an isosceles trapezoid, the intersection point of the diagonals divides them into equal segments.

ОВ = ОС, ОА = ОD.

Then the triangle AOD is isosceles, and the segment OH is the height and median of the triangle, which means AH = DH = AD / 2 = 16/2 = 8 cm. In the triangle AOН, the angle AOН = 45, then the triangle AOН is isosceles and right-angled. AH = OH = 8 cm.

Similarly, in the ВOK triangle: ВK = KO = ВС / 2 = 8/2 = 4 cm.

Then KH = KO + OH = 4 + 8 = 12 cm.

Answer: The height of the trapezoid is 12 cm.