The bases of an isosceles trapezoid are 6 cm and 12 cm. Find the perimeter of the trapezoid
| September 8, 2021 | education
The bases of an isosceles trapezoid are 6 cm and 12 cm. Find the perimeter of the trapezoid if its diagonal is the bisector of an obtuse angle.
Solution:
BCA angle = CAD angle (intersecting angles at the intersection of parallel secant lines)
angle BAC = angle CAD (since by condition the diagonal AC is a bisector)
Therefore, the BCA angle = the BCA angle. Then triangle ABC is isosceles.
AB = BC = 6 cm.
Since the trapezoid is isosceles, then CD = AB = 6 cm.
The perimeter is the sum of all sides, so:
P = 6cm + 6cm + 6cm + 12cm = 30cm
Answer: the perimeter is 30 cm.
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