Find the area of the trapezoid if its base is 5 cm, 17 cm, and the sides are 20 cm and 16 cm, respectively.

The area of an arbitrary trapezoid can be found by the formula:
S = (a + b) / 2 * √ (c ^ 2 – 1/4 ((c ^ 2 – d ^ 2) / (b – a) + b – a) ^ 2),
where S is the area of an arbitrary trapezoid, a is a smaller base, b is a larger base, c and d are the sides.
Substitute the known values into the formula and find the area of the trapezoid:
S = (5 + 17) / 2 * √ (20 ^ 2 – 1/4 ((20 ^ 2 – 16 ^ 2) / (17 – 5) + 17 – 5) ^ 2) = 22/2 * √ ( 400 – 1/4 ((400 – 256) / 12 + 12) ^ 2) = 11 * √ (400 – 1/4 (144/12 + 12) ^ 2) = 11 * √ (400 – 1/4 ( 12 + 12) ^ 2) = 11 * √ (400 – 1/4 * (24) ^ 2) = 11 * √ (400 – 1/4 * 576) = 11 * √ (400 – 576/4) = 11 * √ (400 – 144) = 11 * √256 = 11 * 16 = 176 (cm square).
Answer: S = 176 square cm.