In an isosceles trapezoid, the diagonals are mutually perpendicular, the height of the trapezoid = 18 cm.

| June 27, 2021 | education

In an isosceles trapezoid, the diagonals are mutually perpendicular, the height of the trapezoid = 18 cm. Find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. EK is the middle line. Height BH = 18 centimeters.

2. Since, according to the problem statement, the diagonals of this trapezoid are perpendicular, then, according to its properties, the length of the height of the trapezoid is equal to the length of the middle line:

BH = EK = 18 centimeters.

3. To calculate the area of a geometric figure, we use the formula for calculating the length of the center line:

(BC + AD) / 2 = EK = 18 centimeters.

4. The area of the trapezoid = (BC + AD) / 2 x BH = 18 x 18 = 324 centimeters².

Answer: The area of the trapezoid is 324 centimeters².



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