In a rectangular trapezoid ABCD, the lateral side is AB = 10 cm, the larger base AD = 18 cm, the angle

In a rectangular trapezoid ABCD, the lateral side is AB = 10 cm, the larger base AD = 18 cm, the angle D = 45. Find the area of the trapezoid.

1. From the top of trapezoid C, draw a perpendicular CK to the side AD.

2. We calculate the value of the angle DCК of a right-angled triangle CDK:

180 ° – 90 ° – 45 ° = 45 °.

3. The angles at the base of the CD triangle are equal. Therefore, the CDK triangle is isosceles. CK = KD = 10 cm.

4. We calculate the size of the segment AK:

AK = AD – KD = 18 – 10 = 8 cm.

5. Upper base BC = AK = 8 cm.

6. Calculate the area of the trapezoid ABCD:

AB x (AD + BC) / 2 = 10 x (8 + 18) / 2 = 130 cm ^ 2.

Answer: the area of the trapezium ABCD is 130 cm ^ 2.