# The trapezium

The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.

Result

A =  18.75 cm2

#### Solution:

$b_{ 1 } = 10 \ cm \ \\ b_{ 2 } = 5 \ cm \ \\ \ \\ a_{ 1 }^2 + a_{ 1 }^2 = b_{ 1 }^2 \ \\ a_{ 2 }^2 + a_{ 2 }^2 = b_{ 2 }^2 \ \\ \ \\ a_{ 1 } = b_{ 1 } / \sqrt{ 2 } = 10 / \sqrt{ 2 } = 5 \ \sqrt{ 2 } \ cm \doteq 7.0711 \ cm \ \\ \ \\ a_{ 2 } = b_{ 2 } / \sqrt{ 2 } = 5 / \sqrt{ 2 } \doteq 3.5355 \ cm \ \\ \ \\ A_{ 1 } = \dfrac{ a_{ 1 }^2 }{ 2 } = \dfrac{ 7.0711^2 }{ 2 } = 25 \ cm^2 \ \\ A_{ 2 } = \dfrac{ a_{ 2 }^2 }{ 2 } = \dfrac{ 3.5355^2 }{ 2 } = \dfrac{ 25 }{ 4 } = 6.25 \ cm^2 \ \\ \ \\ A = A_{ 1 }-A_{ 2 } = 25-6.25 = \dfrac{ 75 }{ 4 } = 18.75 = 18.75 \ cm^2$

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Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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