The lengths of the base of an isosceles trapezium are 12 cm and 28 cm, and the length of the lateral side is 10 cm. Calculate the area of the tropezium.
1. The tops of the trapezoid – A, B, C, D. BC = 12 centimeters. AD = 28 centimeters. AB = 10 centimeters. BE – height. S is the area of the parallelogram.
2. According to the properties of an isosceles trapezoid, the length of the segment AE is calculated by the formula:
AE = (AD – AB / 2 = (28 – 12) / 2 = 8 centimeters.
3. BE = √AB² – AE² (by the Pythagorean theorem).
BE = √AB² – AE² = √10² -8² = √100 – 64 = √36 = 6 centimeters.
4. S = AD x BE = 28 x 6 = 168 centimeters².
Answer: S equals 168 centimeters².
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