Find the area of the parallelogram if the height BE drawn from an angle of 135 degrees divides

Find the area of the parallelogram if the height BE drawn from an angle of 135 degrees divides the base AD into segments AE = 6cm ED = 10cm.

1. Vertices of the parallelogram – A, B, C, D. S – area of the parallelogram. ∠В = 135 °.

2. AD = AE + DE = 6 + 10 = 16 centimeters.

3.∠ABE = 135 ° – 90 ° = 45 °.

4. Considering that the total value of the angles of the triangle is 180 °, we calculate

value ∠ВАЕ:

∠ВАЕ = 180 ° – 90 ° – 45 ° = 45 °.

5. BE: AE = tangent ∠BAE tangent 45 ° = 1.

BE = 6 x 1 = 6 centimeters.

6. S = AD x BE = 16 x 6 = 96 centimeters².

Answer: S = 96 centimeters².