In trapezoid ABCD, the bases of BC and AD are 1: 3. Find the area of a trapezoid if the area of a triangle BCD is 2cm ^ 2.

Let the length of the smaller base of the trapezoid be X cm, then, by condition, the length of the larger base will be 3 * X cm.

Let us draw the height DM to the smaller base of the trapezoid.

Then the area of the triangle ВСD will be equal to: Sвсд = ВС * DМ / 2 = X * DМ / 2 = 2 cm.

Since the height DМ is equal to the height ВН, then Svsd = X * ВН / 2 = 2 cm.

Determine the area of the triangle ABD.

Sabd = AD * ВН / 2 = 3 * X * ВН / 2.

In the area of the triangle ABD, the product (X * BH / 2) is the area of the triangle BCD, which is 2 cm2.

Then Sabd = 3 * Svsd = 6 cm2.

Then Strapezium = Savd + Svsd = 6 + 2 = 8 cm2.

Answer: The area of the trapezoid is 8 cm2.