Answer:
Area of shades region [tex]=45[/tex] square inches
Step-by-step explanation:
In the given figure accordingly, we have to find the Area of the shaded region
Area of shaded region= Area of big triangle - Area of the small triangle.
Area of a triangle= [tex]\frac{1}{2} *base*altitude[/tex]
Altitude is the perpendicular height of the triangle from its top to base.
Base of big triangle=12 inches, Altitude of big triangle=6+3= 9 inches
Area of Big triangle
[tex]=\frac{1}{2}* 12*9\\\\=6*9\\\\=54[/tex]
Base of small triangle= 6 inches, Altitude of small triangle= 3 inches
Area of the small triangle=
[tex]=\frac{1}{2} *6*3\\\\=3*3\\\\=9[/tex]
Area of shades region [tex]=54-9\\[/tex]
[tex]=45[/tex] square inches
