Trapezoid MO-5-Z8

Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm2. What is the area of the trapezoid KLMN?

Result

S =  36 cm2

Solution:

a=12 c=4 S1=9 S1=c⋅ h/2 h=2⋅ S1/c=2⋅ 9/4=92=4.5 S=(a+c)⋅ h/2=(12+4)⋅ 4.5/2=36=36 cm2a = 12 \ \\ c = 4 \ \\ S_{ 1 } = 9 \ \\ S_{ 1 } = c \cdot \ h /2 \ \\ h = 2 \cdot \ S_{ 1 }/c = 2 \cdot \ 9/4 = \dfrac{ 9 }{ 2 } = 4.5 \ \\ S = (a+c) \cdot \ h/2 = (12+4) \cdot \ 4.5/2 = 36 = 36 \ cm^2

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