In rectangle ABCD, point E is on side AB, and point F is on side BC. Line segments DE, EF, and DF divide rectangle ABCD into four triangles, as shown in the figure below. The area of triangle ADE is 65 cm2, and side AE measures 13 cm. The area of triangle CDF is 28.5 cm2, and side FC measures 3 cm. What is the area of triangle DEF? Note: The figure is not drawn to scale. Write your answer as a decimal number.

In a rectangle ABCD, E is the midpoint of AD and F is the midpoint of CE. If the area of triangle BDF is 24 sq. cm, what is the area (in sq. cm) of rectangle ABCD?

In triangle ABC, point D and point E are on side BC, as shown in the figure below. The length of side BC is 34 inches. The area of triangle ABC is 170 square inches, the area of triangle ABE is 90 square inches, and the area of triangle ADC is 140 square inches. What is the length of line segment DE? Note: The figure is not drawn to scale.

In triangle ABC, point E lies on AB and point D lies on AC. Lines BD and CE meet at F. The areasof triangles BEF, CDF and BCF are 5, 8, and 10, respectively. What is the area of quadrilateralAEFD?(A) 20 (B) 21(C) 22 (D) 25

In the figure below not drawn to scale, ACED is a rectangle. AB = 20 cm. BC = 18 cm. AD = 25 cm. CE = 25 cm.Find the area of the shaded triangle △BDE.

Let ΔABC be an equilateral triangle. D, E, F are points on the sides such that BD : DC = CE : EA = AF : FB = 2 : 1. If the area of ΔABC is 315 sq. cm, then what is the area (in sq. cm) of the triangle bounded by AD, BE, and CF?