In the trapezoid of ABCD, the smaller base of the BC is 4 cm. A straight line parallel to the side of the CD is drawn

| January 28, 2021 | education

In the trapezoid of ABCD, the smaller base of the BC is 4 cm. A straight line parallel to the side of the CD is drawn through apex B. The perimeter of the resulting triangle is 12 cm. Find the perimeter of the trapezoid.

Let us consider a quadrilateral ВСDН, in which, the ВС is parallel to the НП, since the НП belongs to the base of the AD, and the bases of the trapezium are parallel, and the ВН is parallel to the СD by the condition, therefore, the ВСНD is a parallelogram. Then ВН = СD, ВС = НD = 4 cm.

The perimeter of the trapezoid is:

Ravsd = AB + BC + СD + AD.

Since BP = AН + DН, and СD = ВН then:

P = AB + BC + ВН + AН + DН.

AB + BH + AH is the perimeter of the ABC triangle, which, by condition, is 12 cm.

Then Ptrapezium = Ptreug + BC + DН = 12 + 4 + 4 = 20 cm.

Answer: The perimeter of the trapezoid is 20 cm.



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