The perimeter of parallelogram ABCD is 80 cm and the length of its diagonal AC is 30 cm. Points K and P

univerkov | February 28, 2021 | education

The perimeter of parallelogram ABCD is 80 cm and the length of its diagonal AC is 30 cm. Points K and P are midpoints of sides AB and BC, respectively. Find the perimeter of the pentagon AKPCD

Since points K and P are the middle of the sides AB and BC, the segment KP is the middle line of the triangle ABC. Then KР = AC / 2 = 30/2 = 15 cm.

The perimeter of the parallelogram is: Ravsd = 2 * (AB + BC) = 2 * (AD + CD) = 80 cm.

Then (AB + BC) = (AD + CD) = 40 cm.

AK = ВK, BP = CP, then (ВK + BP) = (AK + CP) = (AB + BC) / 2 = 40/2 = 20 cm.

Rakrsd = (AK + CP) + (AD + CD) + KР = 20 + 40 + 15 = 75 cm.

Answer: The perimeter of the pentagon is 75 cm.

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