Find the area of an isosceles trapezoid if its smaller base is 7 cm. Lateral side 10 cm high 8 cm.

univerkov | June 16, 2021 | education

1. The tops of the trapezoid – A, B, C, D. S – the area of the trapezoid. BC = 7 cm. BE = 8 cm – height to AD.

AB = 10 cm.

2. Calculate the length of the segment AE using the formula of the Pythagorean theorem:

AE = √AB² – BE² = √10² – 8² = √100 – 64 = √36 = 6 cm.

3. We calculate the length of the segment AE using a different formula:

AE = (AD – BC) / 2 (according to the properties of an isosceles trapezoid).

(АD – ВС) / 2 = 6 cm.

AD – BC = 12 cm.

AD = BC + 12 cm = 7 + 12 = 19 cm.

4. S = (AD + BC) / 2 x BE = (19 + 7) / 2 x 8 = 104 cm²

Answer: S is equal to 104 cm².

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