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:

b1=10 cm b2=5 cm  a12+a12=b12 a22+a22=b22  a1=b1/2=10/2=5 2 cm≐7.0711 cm  a2=b2/2=5/2≐3.5355 cm  A1=a122=7.071122=25 cm2 A2=a222=3.535522=254=6.25 cm2  A=A1−A2=25−6.25=754=18.75=18.75 cm2b_{ 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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Following knowledge from mathematics are needed to solve this word math problem:

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

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