Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?

Correct result:

S =  321.9487 cm²

Solution:

$$\begin{gathered} a=35 \\ b=28 \\ d=14 \\ c=11 \\ h>0 \\ {d}^2=x^2+h^2 \\ {b}^2=y^2+h^2 \\ c=a-x-y \\ 14^2=x^2+h^2 \\ 28^2=y^2+h^2 \\ c=35-x-y \\ x=-1\mathrm{/}4=-{\displaystyle \frac{1}{4}}=-0.25 \\ y=97\mathrm{/}4={\displaystyle \frac{97}{4}}=24.25 \\ c=a-x-y=35-(-0.25)-24.25=11 \\ h=\sqrt{d^2-x^2}=\sqrt{14^2-(-0.25{)}^2}\doteq 13.9978\text{ cm } \\ S=(a+c)\cdot h\mathrm{/}2=(35+11)\cdot 13.9978\mathrm{/}2=321.9487{\text{cm}}^2 \end{gathered}$$

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Showing 1 comment:

Evan

How did you come up with x = -0.25 and y = 24.25?

3 years ago  Like

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