Given:
Two figures.
To find:
The area of the shaded regions for both figures.
Solution:
In first figure, the shaded area is a triangle with base 15 units and height 12 units. So, the area of the shaded region is equal to area of the triangle.
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
[tex]A=\dfrac{1}{2}\times 15\times 12[/tex]
[tex]A=\dfrac{180}{2}[/tex]
[tex]A=90[/tex]
Therefore, the area of the shaded region is 90 square units.
In the seconds figure, we need to subtract the area of square from the area of triangle, to get the area of the shaded region.
Area of triangle with base 15 and height 18 is:
[tex]A_1=\dfrac{1}{2}\times 15\times 18[/tex]
[tex]A_1=\dfrac{270}{2}[/tex]
[tex]A_1=135[/tex]
Area of the square with sides 6.
[tex]A_2=(side)^2[/tex]
[tex]A_2=(6)^2[/tex]
[tex]A_2=36[/tex]
Now, the area of the shaded region is:
[tex]A=A_1-A_2[/tex]
[tex]A=135-36[/tex]
[tex]A=99[/tex]
Therefore, the area of the shaded region is 99 square units.
