Isosceles trapezoid

Find the height in an isosceles trapezoid if the area is 520 cm2 and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid.

Correct answer:

h =  26.6667 cm
A =  78.3462 °
B =  78.3462 °
C =  101.6538 °
D =  101.6538 °

Step-by-step explanation:

a=25 cm c=14 cm S=520 cm2  S = 2a+c​⋅ h  h=a+c2⋅ S​=25+142⋅ 520​=380​ cm=26.6667 cm
x=(a−c)/2=(25−14)/2=211​=5.5 cm  tan A = h : x  A=π180°​⋅arctan(h/x)=π180°​⋅arctan(26.6667/5.5)=78.3462∘=78°20′46"
B=A=78.3462=78.3462∘=78°20′46"
C=180−B=180−78.3462=101.6538∘=101°39′14"
D=180−A=180−78.3462=101.6538∘=101°39′14"

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