Question

if x = 7.1 ft, what is the area of the figure shown below? round your answer to the nearest tenth, but do not include \sq ft\ or \ft^2\ with your response. answer 10 formula 0.5 points a small apartment has a 11ft by 10ft bedroom, a 4ft by 4ft bathroom, and a single multi-use 13ft by 14ft living room/kitchen. what is the total square footage (area) of the apartment? provide a numeric answer only. do not include a unit of measure with your response.

Explanation:

First Problem (Area of the Composite Figure)

Step1: Identify the shapes (square and triangle)

The figure is a composite of a square (side \( x \)) and a triangle (base \( x \), height \( x \)).

Step2: Area of the square

Area of square \( = x^2 \). For \( x = 7.1 \), \( 7.1^2 = 50.41 \).

Step3: Area of the triangle

Area of triangle \( = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2}x^2 \). For \( x = 7.1 \), \( \frac{1}{2} \times 7.1^2 = \frac{1}{2} \times 50.41 = 25.205 \).

Step4: Total area

Total area \( = \) Area of square \( + \) Area of triangle \( = x^2 + \frac{1}{2}x^2 = \frac{3}{2}x^2 \). Substitute \( x = 7.1 \): \( \frac{3}{2} \times 50.41 = 75.615 \approx 75.6 \) (rounded to nearest tenth).

Step1: Area of bedroom

Area of bedroom \( = 11 \times 10 = 110 \).

Step2: Area of bathroom

Area of bathroom \( = 4 \times 4 = 16 \).

Step3: Area of living room/kitchen

Area of living room/kitchen \( = 13 \times 14 = 182 \).

Step4: Total area

Total area \( = 110 + 16 + 182 = 308 \).

Answer:

75.6

Second Problem (Total Square Footage of Apartment)