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?

It can be decomposed into the following simplest shapes:

Two Rectangles and one Triangle.

The area is

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:

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

You can identify in the picture that:

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

The formula for the area of a triangle is:

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

In this case:

Then, its area is:

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

It can be decomposed into the following simplest shapes:

Two Rectangles and one Triangle.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

the answer is 1/4

step-by-step explanation: