In isosceles trapezoid ABCD, a straight line is drawn through vertex B, which is parallel to side CD and intersects side AD

univerkov | November 20, 2020 | education

In isosceles trapezoid ABCD, a straight line is drawn through vertex B, which is parallel to side CD and intersects side AD at point N. The perimeter of triangle ABN is 38 cm, CB is 8 cm. Calculate the perimeter of trapezoid ABCD.

BCDN is a parallelogram, since BC is parallel to ND and BN is parallel to CD. Then CD = BN. Perimeter of trapezoid ABCD Pabcd = AB + CD + AN + ND + BC = AB + BN + AN + ND + BC. Since AB + BN + AN = Pabn is the perimeter of triangle ABN, then Pabcd = Pabn + ND + BC = 38 + 8 + 8 = 54 cm.The desired perimeter of trapezoid ABCD is 54 cm.

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