The bases of the trapezoid are 16 and 44 a. Lateral sides 17 and 25. Find the area of the trapezoid.

Decision:
ΔABK: AK = x,
Equation for BK
BK² = h² = 17² – x².
Let’s make an equation for MD.
MD = 44 – 16 – x = 28 – x.
ΔCMD: h² = 25² – (28 – x) ² = 625 – 784 + 56 * x – x².
17² – x² = -159 + 56 * x – x².
289 + 159 = 56 * x.
56 * x = 448.
x = 8, AK = 8 centimeters.
h = √17² – 8² = √289 – 64 = √225 = 15.
Let’s calculate the area of the given trapezoid ABCD.
S (abcd) = ((16 + 44) / 2) × 15 = 30 * 15 = 450 square centimeters (cm²).
Answer: the area of the trapezoid is 450 square centimeters (cm²).