The height of the BC, drawn to the side AD of the parallelogram ABCD. Divides this side into two segments AK

univerkov | July 16, 2021 | education

The height of the BC, drawn to the side AD of the parallelogram ABCD. Divides this side into two segments AK = 7 cm, KD = 15 cm Find the area of the parallelogram if the angle is A = 45 degrees.

1. It is known that the area of a parallelogram is equal to the product of its side by the height lowered to this side.

2. For the parallelogram given in the problem statement, the area is S = AD * BK.

We calculate the value of BK from a right-angled triangle ABK:

BK: AK = tg 45 ° = 1, so BK = AK = 7 cm.

Side AD consists of segments AK and KD, which are 7 cm and 15 cm, respectively, therefore AD = 7 cm + 15 cm = 22 cm.

3. Let’s calculate what the area is equal to

S = 22 cm * 7 cm = 154 cm².

Answer: The area of the parallelogram is 154 cm².

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