Find the area of an isosceles trapezoid if its bases are 12 cm and 6 cm, and the side makes an angle

Find the area of an isosceles trapezoid if its bases are 12 cm and 6 cm, and the side makes an angle of 45 degrees with one of the bases.

1. The tops of the trapezoid – A, B, C, D. ВK – height. The area of the trapezoid is S. BC = 6 cm. AD = 12 cm.

∠А = 45 °.

2. The AK segment, according to the properties of an isosceles trapezium, is calculated by the formula:

AK = (AD – BC) / 2 = (12 – 6) / 2 = 3 cm.

3. We calculate the length of the height BK through the tangent ∠A, which is equal to the quotient of dividing the height of BK – leg of the right-angled triangle ABK by the other leg (AK).

BK: AK = tangent ∠A = tangent 45 ° = 1.

BK = AK x 1 = 3 x 1 = 3 cm.

4. S = (AD + BC) / 2 x BK = (12 + 6/2 x 3 = 9 x 3 = 27 cm².