The heights of the parallelogram drawn from the apex of the obtuse angle of the parallelogram

| January 30, 2021 | education

The heights of the parallelogram drawn from the apex of the obtuse angle of the parallelogram make up an angle of 45. one of the heights divides the side on which it is lowered into 3cm and 7 cm segments, counting from the apex of the acute angle. Find the area of the parallelogram.

1. Vertices of the parallelogram – A, B, C, D. S – area of the parallelogram. The HВ height is drawn to the AD side. The height of the ВK is drawn to the side of the СD. ∠НВК = 45 °.

2. ∠АВН = ∠АВК – ∠НВК = 90 ° – 45 ° = 45 °.

3. We calculate the length of the ВН height through the tangent ∠АВН, equal to the quotient of dividing the AН leg by the ВН height, which is the second leg in the right-angled AВН triangle:

AH: BH = tangent ∠ABН = tangent 45 ° = 1.

BH = AH: 1 = 3: 1 = 3 cm.

4. AD = AН + DН = 3 + 7 = 10 cm.

5. S = AD x ВН = 10 x 3 = 30 cm²



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