Find the area of the parallelogram ABCD if the height B E drawn from the vertices

Find the area of the parallelogram ABCD if the height B E drawn from the vertices of an angle of 135 ° divides the base into segments AE = 6 cm ED = 10 cm

1. S is the area of the parallelogram.

2. ∠ABE = ∠B – ∠CBE = 135 ° – 90 ° = 45 °.

3. ∠ВАЕ = 180 ° – 90 ° – 45 ° = 45 °.

4. We calculate the length of the height BE through the tangent equal to the quotient of division BE (the leg of the right-angled triangle ABE) by AE, which is also the leg of the indicated triangle:

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

BE = AE x 1 = 6 x 1 = 6 centimeters.

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

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

Answer: S equals 96 centimeters².