Find the area of the trapezoid, the bases of which are 14 and 26, the large side is 45 degrees with the base.

An error was made in the problem statement. It is not indicated that trapezoid ABCD is rectangular.

1. A, B, C, D – the tops of the trapezoid. ∠А = 45 °. ∠D = 90 °.

2. Draw from the top B height BE to the side AD.

3. Calculate the degree measure ∠ABE of the right-angled triangle ABE:

∠ABE = 180 ° – 90 ° – 45 ° = 45 °.

The angles at its base AB of triangle ABE are equal. Therefore, the indicated triangle

isosceles

Hence, BE = AE.

3. AE = AD – DE. DE = BC = 14 units.

AE = BE = 26 – 14 = 12 units.

4. Calculate the area (S) of the trapezoid:

S = (BC + AD) / 2 x BE = (14 + 26) / 2 x 12 = 240 units of measurement².

Answer: the area of ​​the trapezoid ABCD is equal to 240 units of measurement².