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, angle C is a right angle. Point D lies on side AB, and point E lies on side BC. The line DE is parallel to side AC. If the length of side AB is 39 units, the length of DE is 8 units, and the length of side AC is greater than the length of side BC, and the area of triangle ABC is 270 square units, what is the length of side BE, in units?

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.

ABC is a triangle with ∠BAC = 120°, and D and E are points on side BC such that DAE is an equilateral triangle. If BD = 8 cm and EC = 32 cm, what is the length (in cm) of DE?

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 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.