Question

PLEASE HELP!!

Aaron drew the figure below for a school art project. What is the total area of the figure?
12 in
3 in.
2 in.. 2.5 in.
4.25 in. 2.75 in.
3 in
4 in.
Use the drop-down menus to complete the sentences to determine the total area of the figure.
Click the arrows to choose an answer from each menu.
The trapezoid has a height of 3 inches, a shorter base measuring Choose... inches, and
a longer base measuring Choose... inches. The total area of the entire figure is
Y
Choose...
square inches.

Answer 1

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,

`\text{Total area of figure=Area of rectangle+Area of trapezoid+Area of square+Area of triangle}`

Taking the shapes one after the other,

For the rectangle, Area of a rectangle is,

`\begin{gathered} \text{Area of rectangle = l}* b \\ l=4\text{ in and b = 2.75 in} \\ =4*2.75=11in^2 \end{gathered}`

For the trapezoid, Area of a trapezoid is,

`\begin{gathered} \text{Area of trapezoid = }(1)/(2)(a+b)h^{} \\ a=2.75\text{ in, b = 4.25 in and h = 3 in} \\ =(1)/(2)(2.75+4.25)(3)=10.5in^2 \end{gathered}`

For the square, Area of a square is,

`\begin{gathered} \text{Area of square = l}^2 \\ l=3\text{ in} \\ =3^2=9in^2 \end{gathered}`

For the triangle, Area of a triangle is,

`\begin{gathered} \text{Area of triangle =}(1)/(2)bh \\ b=2.5\text{ in and h = 2 in} \\ =(1)/(2)*2.5*2=2.5in^2 \end{gathered}`

There the area of the figure will be,

`\text{Area of figure = 11 + 10.5 + 9 + 2.5 =}33in^2`

Hence, the area of the figure is 33in².