Answer:
It can be decomposed into the following simplest shapes:
Two Rectangles and one Triangle.
The area is [tex]242\ ft^2[/tex]
Step-by-step explanation:
You can observe in the picture attached that it can be decomposed into the following simplest shapes:
Two Rectangles.
One Triangle.
The area of the a rectangle can be found with:
[tex]A=lw[/tex]
Where "l" is the length and "w" is the width.
You can identify in the picture that:
[tex]l_A=14\ ft\\w_A=13\ ft-7\ ft=6\ ft\\\\l_B=20\ ft\\w_B=7\ ft[/tex]
Substituing values, you get that the areas of the rectangles A and B are:
[tex]A_A=(14\ ft)(6\ ft)=84\ ft^2\\\\\\A_B=(20\ ft)(7\ ft)=140\ ft^2[/tex]
The formula for the area of a triangle is:
[tex]A=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
In this case:
[tex]b=20\ ft-14\ ft=6\ ft\\\\h=6\ ft[/tex]
Then, its area is:
[tex]A_C=\frac{(6\ ft)(6\ ft)}{2}= 18\ ft^2[/tex]
Then, the total area of carpet that Valerie needs for her project is:
[tex]A_t=A_A+A_B+A_C\\\\A_T=84\ ft^2+140\ ft^2+18\ ft^2\\\\AT=242\ ft^2[/tex]
