In trapezoid ABCD BC and AD bases. BC: AD = 4: 5. triangle area ACD = 35cm. Find the area of a trapezoid

Let the length of the segment BC = 4 * X cm, then the length of the base of AD = 5 * X cm.

Consider triangles ABC and ACD, in which the height of the trapezoid CH is also the height of these triangles.

Savs = BC * CH / 2 = 4 * X * CH / 2 cm2.

Sasd = AD * CH / 2 = 5 * X * CH / 2 cm2.

Let’s find the ratio of the areas of the triangles.

Savs / Sasd = (4 * X * CH / 2) / 5 * X * CH / 2 = 4/5.

Then Saavs / 35 = 4/5.

Sавс = 35 * 4/5 = 28 cm2.

The area of the trapezoid is equal to: Savs = Savs + Sasd = 28 + 35 = 63 cm2.

Answer: The area of the trapezoid is 63 cm2.