Question

applications of area, surface area, and volume: tutorial
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activity
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?

Explanation:

Step1: Decompose the shape

We can split the figure into 1 rectangle and 1 trapezoid (the fewest simple shapes):

• Rectangle: Dimensions $13\ \text{ft} \times 14\ \text{ft}$
• Trapezoid: Bases $7\ \text{ft}$ and $(20-14)=6\ \text{ft}$, height $13\ \text{ft}$

Step2: Calculate rectangle area

Area formula: $A_{\text{rect}} = l \times w$
$A_{\text{rect}} = 13 \times 14 = 182\ \text{sq ft}$

Step3: Calculate trapezoid area

Area formula: $A_{\text{trap}} = \frac{1}{2}(b_1 + b_2)h$
$A_{\text{trap}} = \frac{1}{2}(7 + 6) \times 13 = \frac{1}{2}(13) \times 13 = 84.5\ \text{sq ft}$

Step4: Sum the two areas

Total area = $A_{\text{rect}} + A_{\text{trap}}$
Total area = $182 + 84.5 = 266.5\ \text{sq ft}$

Answer:

Part A:

The figure can be decomposed into 1 rectangle and 1 trapezoid (the fewest simple shapes).

Total Carpet Needed:

$266.5$ square feet