Find the area of a trapezoid whose sides are 17, 10.5, and 10 cm.

1. The tops of the trapezoid A, B, C, D. AB = CD = 10 cm. BC = 5 cm. AD = 17 cm.

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

3. Calculate the length of the segment AE:

AE = (AD – BC) / 2 = (17 – 5) / 2 = 6 cm.

4. We calculate the length of the height BE:

BE = √AB² – AE² = √10² – 6² = √100 – 36 = √64 = 8 cm.

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

S = (BC + AD) / 2 x BE = (5 + 17) / 2 x 8 = 88 cm².

Answer: the area of the trapezoid is 88 cm².