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ivolga24 [154]
3 years ago
15

Valerie is remodeling her home. She decides to replace the old carpet in the living room and wants to know how much carpet she n

eeds. 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?

Mathematics
2 answers:
PIT_PIT [208]3 years ago
7 0

Answer:

It can be decomposed into the following simplest shapes:

Two Rectangles and one Triangle.

The area is 242\ ft^2

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:

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=\frac{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=\frac{(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

valentina_108 [34]3 years ago
7 0

Answer:

It can be decomposed into the following simplest shapes:

Two Rectangles and one Triangle.

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