The area of the parallelogram is 30 roots of 3 cm square, one of the angles is 60 degrees

| May 2, 2021 | education

The area of the parallelogram is 30 roots of 3 cm square, one of the angles is 60 degrees. Find the perimeter of a parallelogram if the length of one side is 6 cm.

1. Vertices of the parallelogram A, B, C, D. ∠A = 60 °. AB = 6 cm.

2. Draw from the top B in height BH to the base of AD.

3. We calculate the length of the segment AH in terms of the cosine ∠A:

AН: AB = cosine ∠A. Cosine 60 ° = 1/2.

AH = AB x 1/2 = 6 x 1/2 = 3 cm.

4. We calculate the length of the ВН height using the Pythagorean theorem:

BH = √AB² – BH² = √6² – 3² = √36 – 9 = √27 = 3√3 cm.

5. Calculate the length of the base AD, using the formula for calculating the area of a parallelogram:

AD x BH = 30√3.

АD = 30√3 / 3√3 = 10 cm.

6. Calculate the perimeter (P) of the parallelogram:

P = 2 x 10 + 2 x 6 = 32 cm.

Answer: the perimeter of the parallelogram is 32 cm.



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