Question

Find the area of the rhombus given below:

• A. 8400 $m^2$
• B. 7200 $m^2$
• C. 9600 $m^2$
• D. 8800 $m^2$

Answer 1

The correct option is C 9600 $m^2$

In $△ABD$, semiperimeter 's' is given by:
s = $\frac{100+160+100}{2}$
= 180 m
Now ,
Area of the triangle ABD is given by :
$ar\left(ABD\right)=\sqrt{s\times (s-a)\times (s-b)\times (s-c)}=\sqrt{180\times (180-100)\times (180-100)\times (180-160)}=\sqrt{180\times (180-100)\times (180-100)\times (180-160)}=\sqrt{180\times \left(80\right)\times \left(80\right)\times \left(20\right)}=4800{\text{m}}^2$
Now, the other triangle also has the same dimensions.
So,
ar(BCD) = 4800 $m^2$ = ar(ABD)
So, the area of the rhombus ABCD = ar(BCD) + ar(ABD)
= 4800 + 4800
= 9600 $m^2$