Answer:
[tex]\huge\boxed{A_{\triangle RST}=9units^2}[/tex]
Step-by-step explanation:
(Look at the picture).
Calculate the area of the rectangle and subtract the areas of red triangles.
The formula of an area of a rectangle:
[tex]A_{\boxed{\ }}=a\cdot b[/tex]
We have:
[tex]a=5,\ b=4[/tex]
substitute:
[tex]A_{\boxed{\ }}=5\cdot4=20[/tex]
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{a\cdot h}{2}[/tex]
substitute:
[tex]A_1=\dfrac{3\cdot3}{2}=\dfrac{9}{2}=4.5\\\\A_2=\dfrac{2\cdot4}{2}=\dfrac{8}{2}=4\\\\A_3=\dfrac{5\cdot1}{2}=\dfrac{5}{2}=2.5\\\\A_1+A_2+A_3=4.5+4+2.5=11[/tex]
Area of ΔRST:
[tex]A_{\triangle RST}=A_{\boxed{\ }}-(A_1+A_2++A_3)[/tex]
substitute:
[tex]A_{\triangle RST}=20-11=9[/tex]
