The figure given have been splitted into four different figures namely rectangle, trapezoid, square and a triangle.
The total area of the figure is the sum of the areas of the shapes above, it is given as,
[tex]\text{Total area of figure=Area of rectangle+Area of trapezoid+Area of square+Area of triangle}[/tex]Taking the shapes one after the other,
For the rectangle, Area of a rectangle is,
[tex]\begin{gathered} \text{Area of rectangle = l}\times b \\ l=4\text{ in and b = 2.75 in} \\ =4\times2.75=11in^2 \end{gathered}[/tex]For the trapezoid, Area of a trapezoid is,
[tex]\begin{gathered} \text{Area of trapezoid = }\frac{1}{2}(a+b)h^{} \\ a=2.75\text{ in, b = 4.25 in and h = 3 in} \\ =\frac{1}{2}(2.75+4.25)(3)=10.5in^2 \end{gathered}[/tex]For the square, Area of a square is,
[tex]\begin{gathered} \text{Area of square = l}^2 \\ l=3\text{ in} \\ =3^2=9in^2 \end{gathered}[/tex]For the triangle, Area of a triangle is,
[tex]\begin{gathered} \text{Area of triangle =}\frac{1}{2}bh \\ b=2.5\text{ in and h = 2 in} \\ =\frac{1}{2}\times2.5\times2=2.5in^2 \end{gathered}[/tex]There the area of the figure will be,
[tex]\text{Area of figure = 11 + 10.5 + 9 + 2.5 =}33in^2[/tex]Hence, the area of the figure is 33in².
