A circle with a radius of 2 cm is inscribed in a trapezoid, the bases of which are 3 cm and 5 cm.

univerkov | September 21, 2021 | education

A circle with a radius of 2 cm is inscribed in a trapezoid, the bases of which are 3 cm and 5 cm. Find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. BC = 8 centimeters. AD = 12 centimeters. BE – height.

2. We calculate the length BE, taking into account that according to the properties of a circle inscribed in a trapezoid, its radius is equal to 1/2 of the height of the trapezoid:

BE / 2 = 4 centimeters.

BE = 4 x 2 = 8 centimeters.

3. The area of the trapezoid = (BC + AD) / 2 x 8 = (3 + 5): 2 x 8 = 32 centimeters².

Answer: The area of the trapezoid is 32 centimeters².

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