# A two-story home measures 50' ft width and 60' ft length on the lower level exterior. The...

## Question:

A two-story home measures 50' ft width and 60' ft length on the lower level exterior. The interior second level measures 50' ft width and 40' ft length. The window casings are 5 inches thick. The attached garage measures 20' wide and 12' in length. What is the living area of the home?

## Living Area:

The living area inside a house includes the area which is habitable including rooms and the basement. But, any accessory area like the garage can not be counted as a living area.

The lower exterior of the house measures: {eq}50 \mathrm{ft} \times 60 \mathrm{ft}. {/eq}

The area of the lower level exterior will be {eq}50 \mathrm{ft} \times 60 \mathrm{ft} = 3000 \mathrm{ft}^2. {/eq}

The window casings are 5 inches thick. Hence, its area should be deducted from the lower exterior area for finding the living area.

The area covered by the window casings can be found by multiplying the width of window casings with the perimeter of the lower level.

The perimeter of the lower level exterior will be: {eq}2 \times (l + b) = 2 \times (50 + 60) = 220 \mathrm{ft.} {/eq}

Now, for the area of window casings, let's first convert inches to feet.

{eq}12 \text{ inches} = 1 \text{ feet} \\[0.2 cm] 12 \times \dfrac{5}{12} = 1 \times \dfrac{5}{12} \text{ feet.} \\[0.2 cm] 5 \text{ inches} = \dfrac{5}{12} \text{ feet.} {/eq}

Now, the area covered by window casings: {eq}220 \times \dfrac{5}{12} = \dfrac{1100}{12} = 91.666... \mathrm{ft}^2. {/eq}

Hence, the living area on the lower level is: {eq}3000 - 91.666 = 2908.334 \mathrm{ft}^2. {/eq}

Now, the interior area on the second level is: {eq}40 \mathrm{ft} \times 50 \mathrm{ft} = 2000 \mathrm{ft}^2. {/eq}

Hence, the total living area can be given as: {eq}2908.334 + 2000 \mathrm{ft}^2 = 4908.334 \mathrm{ft}^2. {/eq}

Measuring the Area of a Rectangle: Formula & Examples

from

Chapter 8 / Lesson 7
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Learn how to find the area of a rectangle. This lesson explains the formula for determining the area of a rectangle and includes examples of its use.