The lengths of the diagonals of the rhombus are 10 cm and 6 cm. Calculate the area of the quadrangle

| June 14, 2021 | education

The lengths of the diagonals of the rhombus are 10 cm and 6 cm. Calculate the area of the quadrangle, the vertices of which are the midpoints of the sides of the rhombus.

Consider the triangle ABC.

According to the condition, points M and H are the midpoints of the sides AB and BC of the rhombus, then the segment MH is the middle line of the triangle ABC, then MH = AC / 2 = 10/2 = 5 cm.

In the triangle ACD KP is also the middle line, KP = AC / 2 = MH = 5 cm.

MN || AC, КP || AC as middle lines, then MH || KP.

Similarly, КМ = НР = ВD / 2 = 6/2 = 3 cm, and КМ || HP.

Since AC _ | _ BD, then KP _ | _ MK, HP _ | _ MH, and then MHPK is a rectangle.

Determine the area of the quadrangle MHPK Smnrk = KM * KP = 3 * 5 = 15 cm2.

Answer: The area of the quadrangle is 15 cm2.



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