Find the area of an isosceles trapezoid if its bases are 4 cm and 10 cm, and the acute angle is 45 degrees.

1. The tops of the trapezoid – A, B, C, D. S – the area of the trapezoid. ∠А = 45 °. BC = 4 centimeters. BP = 10 centimeters. VK – height.

2. According to the properties of an isosceles trapezoid, the segment AK = (AD – BC) / 2 = (10 – 4) / 2 = 3 centimeters.

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

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

BK = AK x 1 = 3 x 1 = 3 centimeters.

4. S = (AD + BC) / 2 x BK = (10 + 4) / 2 x BK = 7 x 3 = 21 centimeters².