In a parallelogram, the smaller height and the smaller side are 9 cm and √82 cm, respectively.

| September 1, 2021 | education

In a parallelogram, the smaller height and the smaller side are 9 cm and √82 cm, respectively. Large diagonal 15 cm. Find the area of the parallelogram.

1. A, B, C, D – the tops of the parallelogram. BH = 9 cm – lower height. AB = √82 cm – the smaller side. AC = 15 cm – large diagonal.

2. Let us draw the height CM for the continuation of the side AD.

3. Calculate the length of the DM segment using the Pythagorean theorem:

DM = √СD² – CM².

In accordance with the properties of the parallelogram, SD = AB = √82 cm.

CM = BH = 9 cm.

DM = √ (√82) ² – 9² = √82 – 81 = 1 cm.

4. Calculate the length of AM:

AM = √AC² – CM² = √15² – 9² = √225 – 81 = √144 = 12 cm.

5. AD = AM – DM = 12 – 1 = 11 cm.

We calculate the area (S) of a given parallelogram:

S = AD x BH = 11 x 9 = 99 cm².

Answer: the area of ​​a given parallelogram is 99 cm².



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