The vertex B of the rhombus ABCD is connected to the middle of the side AD – by the point G, and the vertex C

| February 21, 2021 | education

The vertex B of the rhombus ABCD is connected to the middle of the side AD – by the point G, and the vertex C of the rhombus ABCD is connected to the midpoint of the segment BG – by the point F. It is required to find: the area of the quadrilateral GFCD, if it is known that the area of the rhombus ABCD is 28 sq. cm.

Let’s carry out additional constructions. We draw the diagonals of the rhombus AC and ВD and connect the point G and the vertex C.

The diagonal of the rhombus ВD we divide the area of the rhombus in half, then Savd = 28/2 = 14 cm2.

The segment BG is the median of the AВD triangle, then Sawg = Sawd / 2 = 14/2 = 7 cm2.

Similarly Sasd = Savsd / 2 = 14 cm2, Sgd = Sasd / 2 = 7 cm2.

Then the area Svgc = Savsd – Sawg – Scgd = 28 – 7 – 7 = 14 cm2.

Since СF is the median of the triangle BCG, then Scfg = Sbgc / 2 = 14/2 = 7 cm2.

Then Sgfсд = Sсgд + Sсfg = 7 + 7 = 14 cm2.

Answer: The area of the GFCL quadrangle is 14 cm2.



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