The rhombus

The area of the rhombus is: $$A=\frac{D \cdot d}{2}$$

Its perimeter is: $$ P=4 \cdot l$$

Calculate the area of a rhombus with $D = 1 \ m$ and $l = 0,7 \ m$

• We find $d$ using the Pythagorean theorem using $D$ and $l$:

$$ l^2= \Big(\frac{d}{2}\Big)^2 +\Big( \frac {D}{2}\Big)^2 \\ \Big(\frac{d}{2}\Big)^2= l^2-\Big(\frac{D}{2}\Big)^2 \\\Big(\frac{d}{2}\Big)^2=0,7^2 \ m^2-0,5^2 \ m^2=0,24 \ m^2 \\ d= 2 \sqrt{0,24} \ m = 0,98 \ m $$

• The area is: $$A=\frac{1 \ m \cdot 0'98 \ m}{2}=0,49 \ m^2$$

And so, the area of the rhombus is: $0,49 \ m^2$.