In an isosceles trapezoid, the diagonal is 10 cm and the height is 6 cm. Find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. Diagonal AC = 10 centimeters. Height CH = 6 centimeters.

2. We calculate the length of the leg AH of the right-angled triangle ACH using the formula of the theorem

Pythagoras:

AH = √AC² – CH² = √10² – 6² = √100 – 36 = √64 = 8 centimeters.

3. According to the properties of an isosceles trapezoid, (BP + BC) / 2 = AH = 8 centimeters.

4. The area of the trapezium = (BP + BC) / 2 x CH = 8 x 6 = 48 centimeters².

The area of the ABCD trapezoid is 48 centimeters².