In the trapezoid ABCD AD – a large base. Through the vertex B, a straight line is drawn, parallel to CD

| July 3, 2021 | education

In the trapezoid ABCD AD – a large base. Through the vertex B, a straight line is drawn, parallel to CD until the intersection with AD at point E. It is known that BC = 7cm, AE = 4cm Find a) the length of the midline of the trapezoid; b) the perimeter of the trapezoid, if the perimeter of the triangle ABE is 17cm

The quadrilateral BCDE is a parallelogram, since its opposite sides are parallel, then DE = BC = 7 cm.

Determine the length of the larger base. AD = AE + DE = 4 + 7 = 11 cm.

Let’s calculate the length of the middle line of the trapezoid.

MH = (BC + AD) / 2 = (7 + 11) / 2 = 9 cm.

The perimeter of the triangle is equal to: Rave = (AB + BE + AE) = 17 cm.

The perimeter of the trapezium AVSD is equal to: Ravsd = (AB + BC + CD + AD).

Since CD = BE, and AD = AE + DE, then Ravsd = (AB + BE + AE) + BC + DE = 17 + 7 + 7 = 31 cm.

Answer: The middle line is 9 cm, the perimeter is 31 cm.



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