A rhombus 2

A rhombus have sides of 170 meters and diagonal of 300 meters. What is the area of the rhombus?

Correct answer:

A =  24000 m²

Step-by-step explanation:

$$\begin{gathered} a=170\text{ m } \\ d=300\text{ m } \\ \mathrm{\Delta }a-a-d \\ s={\displaystyle \frac{1}{2}}\cdot (a+a+d)={\displaystyle \frac{1}{2}}\cdot (170+170+300)=320\text{ m } \\ {S}_1=\sqrt{s\cdot (s-a)\cdot (s-a)\cdot (s-d)}=\sqrt{320\cdot (320-170)\cdot (320-170)\cdot (320-300)}=12000{\text{m}}^2 \\ A=2\cdot S_1=2\cdot 12000=24000{\text{m}}^2 \end{gathered}$$

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