Find the perimeter of a rectangular trapezoid, the bases of which are 14 cm and 30 cm

Find the perimeter of a rectangular trapezoid, the bases of which are 14 cm and 30 cm, and the large diagonal is the bisector of the right angle.

1. The tops of the trapezoid – A, B, C, D. ∠A = ∠B = 90 °. ВС = 14 cm. АD = 30 cm. СН – height.

P is the perimeter.

2. ∠АВD = 90 °: 2 = 45 °, since the bisector ВD divides the angle ∠В into two angles of equal magnitude.

3. We calculate the length of the side AB through the tangent ∠ABD:

AD: AB = tangent ∠ABD = tangent 45 ° = 1.

AB = AD: 1 = 30: 1 = 30 cm.

4. BC = AH = 14 cm, AB = CH = 30 cm.

5.DН = АD – АН = 30 – 14 = 16 cm.

6. СD = √30² + 16² = √900 + 256 = √1156 = 34 cm.

7.P = AB + BC + C + AD = 30 + 14 + 16 + 30 = 90 cm.