【Haichuan Teahouse】Brain-teasing Series: Keeping things straight and aligned is important
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Title: As shown in the figure, quadrilateral ABCD is a right trapezoid. Point E is the midpoint of diagonal AC. It is given that ED is perpendicular to CD, and the area of triangle CDE is 4. Find the area of the trapezoid.
The area is 24. Extending DE to intersect AB at F, △AEF and △CED are equal (right angles, equal opposite sides, equal hypotenuses); therefore, DE = EF, and CD = AF = BF. The area of △CDE = CD * DE / 2 = 4. Using the formula for the area of a trapezoid, we get 24
Point E is the midpoint of diagonal AC; it is given that ED is perpendicular to CD, which thus defines the condition
This post was last edited by Yang Qing on 2021-9-7 08:31. It indeed equals 24; by drawing auxiliary lines, two rectangles are formed. Since the red rectangle’s quarter equals 4, the green triangle is equal to 8. The trapezoid equals 24!
It is divided into six triangles, each with an area of 4.