The perimeter of an isosceles trapezoid is 32 cm, the lateral side is 5 cm, the area is 44 cm2.

univerkov | August 15, 2021 | education

The perimeter of an isosceles trapezoid is 32 cm, the lateral side is 5 cm, the area is 44 cm2. Find the height of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. AB = BC = 5 centimeters. VK – height (drawn to the base of AD).

2. We calculate the total length of the bases using the formula for calculating the perimeter (P) of the trapezoid:

P = BC + AB + AD + BC = 32 cm.

BC + AB = 5 + 5 = 10 centimeters.

AD + BC = 32 – 10 = 22 centimeters.

3. We calculate the length of the height BK, using the formula for calculating S – area.

S = BK x (AD + BC) / 2 = 44 centimeters².

22: 2 x BK = 44.

BK = 44: 11 = 4 centimeters.

Answer: The height of the trapezoid is 4 centimeters.

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