In an isosceles trapezoid, the base is 8 and 22 cm and the side is 25 cm. Find the area.

univerkov | May 13, 2021 | education

1. M, N, K, P – the tops of the trapezoid. Smaller base NK = 8 centimeters. Larger base MР = 22 centimeters. Lateral side МN = 25 centimeters. NE – height to the base of the MP.

2. In accordance with the properties of an isosceles trapezoid, the segment ME = (MP – NK) / 2 =

(22 – 8): 2 = 7 centimeters.

3. Height NE = √МN² – ME² = √25² – 7² = √625 – 49 = √576 = 24 centimeters.

4. Area of the trapezoid = (NK + MP) / 2 x NE = (8 + 22): 2 x 24 = 15 x 24 = 360 centimeters².

Answer: the area of the trapezoid is 360 centimeters².

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