In an isosceles trapezoid, the base angle is 135 degrees, the height is 12 cm

In an isosceles trapezoid, the base angle is 135 degrees, the height is 12 cm, and the larger base is 40 cm. Find the area of the trapezoid.

1. A, B, C, D tops of the trapezoid. The angle is denoted by the symbol ∠. BH height. ∠АВD = 135 °. Larger base АD = 40 cm.

2. ∠АВН = 135 ° – 90 ° = 45 °.

3.∠ВАH = 180 – ∠АВH – ∠АHВ = 180 ° – 45 ° – 90 ° = 45 °.

4. ∠ВАH = ∠ABH. Therefore, triangle ABH is isosceles. Hence, BH = AH = 12 cm.

5. The length of AH is calculated by the formula:

AH = (AD – BD) / 2.

6. Calculate the length of the smaller base BD:

ВD = АD – 2АН = 40 – 2 x 12 = 16 cm.

7. Area of the trapezoid = (AC + BD) / 2 x BH = (40 + 16) / 2 x 16 = 448 cm ^ 2.