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1. Area of the wall (including door): $\frac{391}{4}$ square feet 2. Area of the door: $\frac{81}{4}$ square feet 3. Yes, Amelia has enough paint left (the paintable area is 77.5 …

分類: geometry 更新時間: 2026-02-09

題目

tips for success• read the assignment carefully and make sure you answer each part of the question or questions.• check your work when youre done.your assignmentamelia is painting her room. she has one wall left (shown in the figure) and only $\frac{1}{4}$ gallon of paint, which will cover about 100 square feet. does she have enough paint left?$11\frac{1}{2}$ feet$8\frac{1}{2}$ feet3 feet$6\frac{3}{4}$ feet1. find the area of the wall, including the door. leave your answer as an improper fraction. (2 points)2. find the area of the door. leave your answer as an improper fraction. (2 points)

解題步驟

  1. Understand the question

    tips for success• read the assignment carefully and make sure you answer each part of the question or questions.• check your work when youre done.your assignmentamelia is painting her room. she has one wall left (shown in the figure) and only $\frac{1}{4}$ gallon of paint, which will cover about 100 square feet. does she have enough paint left?$11\frac{1}{2}$ feet$8\frac{1}{2}$ feet3 feet$6\frac{3}{4}$ feet1. find the area of the wall, including the door. leave your answer as an improper fraction. (2 points)2. find the area of the door. leave your answer as an improper fraction. (2 points)

  2. Explanation

    Step1: Convert mixed numbers to improper fractions

    Wall length: $11\frac{1}{2} = \frac{23}{2}$ feet, wall height: $8\frac{1}{2} = \frac{17}{2}$ feet
    Door width: $3 = \frac{3}{1}$ feet, door height: $6\frac{3}{4} = \frac{27}{4}$ feet

    Step2: Calculate wall area (including door)

    Area = length × height
    $\text{Wall Area} = \frac{23}{2} \times \frac{17}{2} = \frac{391}{4}$ square feet

    Step3: Calculate door area

    Area = width × height
    $\text{Door Area} = \frac{3}{1} \times \frac{27}{4} = \frac{81}{4}$ square feet

    Step4: Calculate paintable area

    $\text{Paintable Area} = \frac{391}{4} - \frac{81}{4} = \frac{310}{4} = \frac{155}{2} = 77.5$ square feet

    Step5: Compare to paint coverage

    Paint covers 100 square feet, $77.5 < 100$

  3. Final answer
    1. Area of the wall (including door): $\frac{391}{4}$ square feet
    2. Area of the door: $\frac{81}{4}$ square feet
    3. Yes, Amelia has enough paint left (the paintable area is 77.5 square feet, which is less than the 100 square feet her paint can cover).

答案

Explanation

Step1: Convert mixed numbers to improper fractions

Wall length: $11\frac{1}{2} = \frac{23}{2}$ feet, wall height: $8\frac{1}{2} = \frac{17}{2}$ feet
Door width: $3 = \frac{3}{1}$ feet, door height: $6\frac{3}{4} = \frac{27}{4}$ feet

Step2: Calculate wall area (including door)

Area = length × height
$\text{Wall Area} = \frac{23}{2} \times \frac{17}{2} = \frac{391}{4}$ square feet

Step3: Calculate door area

Area = width × height
$\text{Door Area} = \frac{3}{1} \times \frac{27}{4} = \frac{81}{4}$ square feet

Step4: Calculate paintable area

$\text{Paintable Area} = \frac{391}{4} - \frac{81}{4} = \frac{310}{4} = \frac{155}{2} = 77.5$ square feet

Step5: Compare to paint coverage

Paint covers 100 square feet, $77.5 < 100$

Answer

  1. Area of the wall (including door): $\frac{391}{4}$ square feet
  2. Area of the door: $\frac{81}{4}$ square feet
  3. Yes, Amelia has enough paint left (the paintable area is 77.5 square feet, which is less than the 100 square feet her paint can cover).

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Question Analysis

Subject mathematics
Sub Subject geometry
Education Level middle school
Difficulty unspecified
Question Type with image, calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T19:50:42

OCR Text

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tips for success• read the assignment carefully and make sure you answer each part of the question or questions.• check your work when youre done.your assignmentamelia is painting her room. she has one wall left (shown in the figure) and only $\frac{1}{4}$ gallon of paint, which will cover about 100 square feet. does she have enough paint left?$11\frac{1}{2}$ feet$8\frac{1}{2}$ feet3 feet$6\frac{3}{4}$ feet1. find the area of the wall, including the door. leave your answer as an improper fraction. (2 points)2. find the area of the door. leave your answer as an improper fraction. (2 points)

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mathematicsgeometrywith image, calculationmiddle schoolturns-1

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