Question

Which decimal best represents the ratio of the shaded area to the area of the entire square

Answer 1

Solution:

Given the square;

Each interior angle of a square is 90 degrees. Thus, the shaded region is a right angle given as;

Thus, the area of the shaded region is;

$\begin{gathered} A=\frac{1}{2}bh \\ \\ Where; \\ b=base,h=height \\ \\ b=2,h=2 \end{gathered}$

Then;

$\begin{gathered} A=\frac{1}{2}(2)(2) \\ \\ A=2\text{ }square\text{ }units \end{gathered}$

Also, the area of the entire square is;

$\begin{gathered} A=l^2 \\ \\ Where; \\ l=side\text{ }length \\ \\ l=4 \end{gathered}$

Then;

$\begin{gathered} A=4^2 \\ \\ A=16\text{ }square\text{ }units \end{gathered}$

Thus, the ratio R, of the shaded area to the entire square is;

$\begin{gathered} R=\frac{2}{16} \\ \\ R=0.125 \end{gathered}$

ANSWER: 0.125