# The perimeter of the parallelogram is 72 dm, the heights are 3 dm and 9 dm. Find the area of a parallelogram

July 29, 2021 | education

| 1. A, B, C, D – the tops of the parallelogram. P is the perimeter. S – area. Height BH = 3 dm and BK = 9 dm.

2. S = AD x BH. S = CD x BK.

AD x BH = CD x BK. AD x 3 = CD x 9.

AD = 9СD / 3.

3. To calculate the lengths of the sides of a parallelogram, we use the formula for calculating its perimeter:

P = 2AD + 2CD = 72 dm.

AD + CD = 36 dm. We substitute here (9СD / 3) instead of АD:

9СD / 3 + СD = 36.

12СD / 3 = 36.

CD = 9 dm.

AD = 9СD / 3 = 9 x 9: 3 = 27 dm.

S = AD x BH = 27 x 3 = 81 dm².

Answer: S is equal to 81 dm².

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