In square ABCD of area 12, the midpoint of side AD is marked – point E. By F we denote the point of intersection

| August 9, 2021 | education

In square ABCD of area 12, the midpoint of side AD is marked – point E. By F we denote the point of intersection of AC and BE. Find the area of the quadrilateral EFCD.

Since ABCD is a square, the length of its sides will be: AB = BC = SD = AD = √Savsd = √12 = 2 * √3 cm.

Triangles BFC and AFE are similar in two angles, with a similarity coefficient K = BC / AE = 2.

Then the height KF / HF = 2/1. KF = 2 * HF.

KF + HF = KH = 2 * √3 cm.

2 * HF + HF = 3 * HF = 2 * √3 cm.

HF = 2 * √3 / 3 cm.

Determine the area of the triangle AFE.

Safe = AE * HF / 2 = (√3 * 2 * √3 / 3) / 2 = 1 cm2.

The AC diagonal divides the square into two equal triangles.

Sasd = Savsd / 2 = 12/2 = 6 cm2.

Then Sefcd = Sacd – Safe = 6 – 1 = 5 cm2.

Answer: The area of the EFСD quadrangle is 5 cm2.



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