Question

Valerie is remodeling her home. She decides to replace the old carpet in the living room and wants to know how much carpet she needs. You can see from the diagram of the living room that this is not a simple shape. Complete the steps below to find the area of the room, which is the amount of carpet Valerie needs for her project.

Part A
Help Valerie decompose the shape into the fewest simple shapes. Which shapes can you divide the figure into? How many of each shape do you get?

Answer 1

It can be decomposed into the following simplest shapes:

Two Rectangles and one Triangle.

The area is
`242\ ft^2`

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:

`A=lw`

Where "l" is the length and "w" is the width.

You can identify in the picture that:

`l_A=14\ ft\\w_A=13\ ft-7\ ft=6\ ft\\\\l_B=20\ ft\\w_B=7\ ft`

Substituing values, you get that the areas of the rectangles A and B are:

`A_A=(14\ ft)(6\ ft)=84\ ft^2\\\\\\A_B=(20\ ft)(7\ ft)=140\ ft^2`

The formula for the area of a triangle is:

`A=(bh)/(2)`

Where "b" is the base and "h" is the height.

In this case:

`b=20\ ft-14\ ft=6\ ft\\\\h=6\ ft`

Then, its area is:

`A_C=((6\ ft)(6\ ft))/(2)= 18\ ft^2`

Then, the total area of carpet that Valerie needs for her project is:

`A_t=A_A+A_B+A_C\\\\A_T=84\ ft^2+140\ ft^2+18\ ft^2\\\\AT=242\ ft^2`