Given: The area of a square as 9 square units
To Determine: The length and the width
Solution
The area of a square is calculated as
[tex]Area(square)=length^2[/tex]
Substitute the given
[tex]\begin{gathered} length^2=9 \\ length=\sqrt{9} \\ length=3units \end{gathered}[/tex]
Please note that length and the width of a square are the same
Hence, the length and the width is both 3 units
(b) The area of the square is
[tex]\begin{gathered} Area(square)=l^2 \\ Where\text{ l is the length and width} \end{gathered}[/tex]
(c) Let us divide the square into half
(d) From the above, all the sides are equal, the diagonal is BD. The diagonal divides the square into two equal parts
Each of the parts is a triangle. Therefore, the two congruent shapes made is a triangle
(e) The area of a triangle can be solved using the formula below
[tex]Area(triangle)=\frac{1}{2}\times base\times height[/tex]
Let us consider triangle BCD, DC is the base and BC is the height. Therefore
[tex]\begin{gathered} Area(triangle)=\frac{1}{2}\times3\times3 \\ Area(triangle)=\frac{9}{2}=4.5squareunits \end{gathered}[/tex]
Hence, the area of the triangle is 4.5 square units
