Find the area of the parallelogram if its perimeter is 32 cm, and the heights are 2 cm and 6 cm.

univerkov | June 25, 2021 | education

1. Vertices of the parallelogram – A, B, C, D. S – area of the parallelogram. P is the perimeter of the parallelogram. BE = 2 cm – the height drawn to the AD side. BK = 6 cm – the height drawn to the side of the CD.

2. S = AD x BE = 2AD.

S = CD x BK = 6CD.

2AD = 6CD.

AD = 3СD.

3.P = 2 (AD + CD) = 32 cm.

АD + СD = 16 cm.Replace AD in this expression with 3СD:

3СD + СD = 16 cm.

CD = 4 cm.

AD = 3 x 4 = 12 cm.

4. S = AD x BE = 12 x 2 = 24 cm² or S = CD x BK = 4 x 6 = 24 cm².

Answer: S equals 24 cm²

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