In an isosceles trapezoid ABCD, the sides are 13 cm. The bases are 6 and 16 cm. Find the area of the trapezium.

univerkov | September 16, 2021 | education

1. A, B, C, D – the tops of the trapezoid. Lateral side AB = 13 cm. Base BC = 6 centimeters.

Base AD = 16 centimeters. BE – the height drawn to the base of AD.

2. According to the properties of an isosceles trapezoid, the segment AE = (AD – BC) / 2 = (16 – 6): 2 = 5 centimeters.

3. Height BE = √AB² – AE² = √13² – 5² = √169 – 25 = √144 = 12 centimeters.

4. Area of the trapezoid = (AD + BC) / 2 x BE = (16 + 6): 2 x 12 = 11 x 12 = 132 centimeters².

Answer: The area of the trapezoid is 132 centimeters².

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