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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