Question

if the area of the square ABCD is 100 mm square and the area of the rhombus cdef is 80mm squared, what is the area of the Shaded region! explain your reasoning

Answer 1

Given the area of a square = 100mm square

Also the area of a rhombus = 80mm square

$\begin{gathered} Areaofsquare=100\operatorname{mm} \\ \text{length of the side =l} \\ A=l^2 \\ 100=l^2 \\ l=\sqrt[]{100}=10\operatorname{mm} \end{gathered}$

$\begin{gathered} Areaofrhombus=80\operatorname{mm} \\ so\text{ the altitude =}\frac{80}{10}=8\operatorname{mm} \\ GF=\sqrt[]{10^2-8^2} \\ GF=\sqrt[]{36}=6\operatorname{mm} \end{gathered}$

$\begin{gathered} Areaoftriangle\text{ GFD=}\frac{1}{2}bh \\ =\frac{1}{2}\times6\times8=\frac{48}{2}=24\operatorname{mm} \end{gathered}$

To solve for the area of the shaded region , you will calcuate the area of the triangle out of the two shape, then subtract the area of the triangle from the rhombus and also from the square.

$\begin{gathered} Areaofshadedregion\text{ = }100-(80-24) \\ =100-56 \\ =44\operatorname{mm} \end{gathered}$

Hence the area of the Shaded region = 44mm square