In an isosceles trapezoid, the bases are 2 and 10, and one of the angles between

In an isosceles trapezoid, the bases are 2 and 10, and one of the angles between the lateral side and the base is 45 degrees. Find the area of the trapezoid

1. A, B, C, D – the tops of the trapezoid. BC = 2 units. BP = 10 units.

BE – height. S – area. ∠А = 45 °.

2. We calculate the length of the segment AE of the base of AD:

AE = (AD – BC) / 2 (according to the properties of an isosceles trapezoid).

AE = (10 – 2) / 2 = 4 units.

3. BE / AE = tangent ∠A = tangent 45 ° = 1.

BE = AE x 1 = 4 x 1 = 4 units.

4. S = (АD + ВС) / 2 х BE = (10 + 2) / 2 х 4 = 24 units of measurement².

Answer: S equals 24 units².