Four sides of trapezoid

Calculate the area of the ABCD trapezoid with sides a = 65 cm, b = 29 cm, c = 40 cm, d = 36 cm

Correct answer:

S =  1512 cm²

Step-by-step explanation:

$$\begin{gathered} a=65\text{ cm } \\ b=29\text{ cm } \\ c=40\text{ cm } \\ d=36\text{ cm } \\ {k}_1={\displaystyle \frac{a+c}{4\cdot (a-c)}}={\displaystyle \frac{65+40}{4\cdot (65-40)}}={\displaystyle \frac{21}{20}}=1.05 \\ {S}_1=\sqrt{(a+b-c+d)\cdot (a-b-c+d)\cdot (a+b-c-d)\cdot (-a+b+c+d)}=\sqrt{(65+29-40+36)\cdot (65-29-40+36)\cdot (65+29-40-36)\cdot (-65+29+40+36)}=1440{\text{cm}}^2 \\ S=k_1\cdot S_1=1.05\cdot 1440=1512{\text{cm}}^2 \end{gathered}$$

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