ABCD-parallelogram AB = 12 cm АС = 16 cm vertex D is 4 cm away from AC find:

| August 12, 2021 | education

ABCD-parallelogram AB = 12 cm АС = 16 cm vertex D is 4 cm away from AC find: a) S parallelogram b) distance from point D to AB

1. From the vertex D we draw a perpendicular DH to the diagonal AC. Its length is the distance from the top of D to the AC. DH = 4 centimeters.

2. Calculate the area of ​​the triangle ACD:

Area ΔАСD = АС х DH / 2 = 16 х 4/2 = 32 centimeters².

3. According to the properties of a parallelogram, its diagonal divides this geometric figure into 2 equal triangles:

ΔАСD = ΔАВС.

4. Consequently, the area (S) of the parallelogram ABCD = 32 x 2 = 64 centimeters².

5. From the vertex D draw a perpendicular DK to the side of the parallelogram AB. Its length is the distance from the top D to AB.

6. Calculate the length DK using the formula for the area of ​​a parallelogram (S):

S = AB x DK.

DK = S: AB = 64: 12 = 16/3 = 5 1/3 centimeters.

Answer: the area of ​​the parallelogram is 64 centimeters², the distance from the top of D to the side AB is 5 1/3 centimeters.



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