# Isosceles trapezoid

Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.

Correct result:

S =  420 cm2

#### Solution:

$S = (a+c)h/2 \ \\ \ \\ a_1^2 = b^2 - h^2 \ \\ a_1 = \sqrt{b^2 - h^2} = \sqrt{ 13^2 - 12^2} = 5 \ cm \ \\ a = c+2a_1 \ \\ a/c = 4/3 \ \\ (c+2a_1)c = 4/3 \ \\ 3(c+2a_1) = 4c \ \\ 6a_1 = c \ \\ c = 6a_1 = 6 \cdot 5 = 30 \ cm \ \\ a = c + 2a_1= 30 + 2\cdot 5 = 40 \ cm \ \\ \ \\ S = (a+c)h/2 = (40 + 30) \cdot 12 /2 = 420 \ \text{cm}^2 \ \\$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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