In an isosceles trapezoid, the upper base is 10 cm, the height is 12 cm, one of the corners

univerkov | May 30, 2021 | education

In an isosceles trapezoid, the upper base is 10 cm, the height is 12 cm, one of the corners is 135 degrees. Find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. ВС = 10 cm. Height ВН = 12 cm. ∠С = 135 °.

2.∠А = 180 – ∠С = 180 ° – 135 ° = 45 °.

3. BH: BH = tangent 45 ° = 1.

BH = 12 x 1 = 12 cm.

4. ∠АВН = 180 ° – 90 ° – 45 ° = 45 °.

5. AH: BH = tangent 45 ° = 1.

AH = 12 x 1 = 12 cm.

6. According to the properties of an isosceles trapezoid, the segment AH = (AD – BC) / 2.

AD – BC = AH x 2 = 12 x 2 = 24 cm.

AD = BC + 24 = 10 + 24 = 34 cm.

7. Area of the trapezoid = (AD + BC) / 2 x BH = (34 + 10): 2 x 12 = 22 x 12 = 264 cm²

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