In an isosceles trapezoid, the obtuse angle is 135 degrees, the smaller base is 4cm

In an isosceles trapezoid, the obtuse angle is 135 degrees, the smaller base is 4cm, and the height is 2cm. find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. ВС = 4 cm. ∠В = 135 °. Height BE = 2 cm. S – trapezoid area.

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

3. We calculate the length of the segment AE in terms of one of the trigonometric functions ∠ABE (tangent):

AE / BE = tangent 45 ° = 1.

AE = BE x 1 = 2 x 1 = 2 cm.

4. AE = (AD – BC) / 2.

5. Using this formula, we calculate the length of the base of blood pressure:

(AD – BC) = 2 x AE = 2 x 2 = 4.

AD = 4 + 4 = 8 cm.

6. S = (AD + BC) / 2 x BE = (8 + 4) / 2 x 2 = 12 cm².

Answer: S equals 12 cm².