# In an isosceles trapezoid ABCD, the diagonals are mutually perpendicular

**In an isosceles trapezoid ABCD, the diagonals are mutually perpendicular Find the area of the trapezoid if the diagonal is AC = 6cm.**

The diagonal BD of the trapezoid divides it into triangles ABD and BCD, the sum of the areas of which is equal to the area of the trapezoid.

Since the diagonals of the trapezoid are perpendicular, the AO segment is the height of the ABD triangle, and the CO segment is the height of the BCD triangle.

Determine the areas of the triangles.

Savd = BD * AO / 2.

Svsd = BD * CO / 2.

Then Str = Savd + Svsd = (BD * AO / 2) + (BD * CO / 2) = (BD / 2) * (AO + CO).

ОА + СО = АС = 6 cm, and since the diagonals of an isosceles trapezoid are equal, then ВD = АС = cm, then:

Str = 6 * 6/2 = 18 cm2.

Answer: The area of the trapezoid is 18 cm2.