In trapezoid ABCD, the bases BC and AD are 2cm and 8cm, and the diagonal AC is 4cm.

In trapezoid ABCD, the bases BC and AD are 2cm and 8cm, and the diagonal AC is 4cm. In what ratio does the AC diagonal divide the area of the trapezoid?

Let us draw the height CH from the vertex C of the trapezoid.

Then the area of the trapezoid is determined by the formula:

Savsd = (BC + AD) * CH / 2 = 10 * CH / 2 = 5 * CH cm2.

The area of the triangle ACD is equal to:

Sasd = AD * CH / 2 = 8 * CH / 2 = 4 * CH.

The area of the triangle ABC is equal to:

Savs = BC * CH / 2 = 2 * CH / 2 = CH.

Savs / Sasd = CH / 4 * CH = 1/4.