# In a parallelogram, ABCD, BK and BT are heights. Points K and T belong to sides AD and DC

October 1, 2021 | education

| **In a parallelogram, ABCD, BK and BT are heights. Points K and T belong to sides AD and DC, BK = 10 cm, BT = 9cm, TC = 12cm. find the area of the parallelogram**

1.Calculate the length of the BC side, which in the rectangular ΔВСТ is the hypotenuse, and the BT height and the CT segment are legs:

BC = √BT² + ST² = √9² + 12² = √81 + 144 = √225 = 15 centimeters.

2. ВС = АD = 15 centimeters, since the opposite sides of the parallelogram are equal.

3. Calculate the area of the parallelogram (S):

S = AD x BK = 15 x 10 = 150 centimeters².

Answer: S equals 150 centimeters².

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