Rectangular and Area Problems Quiz
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Rectangular and Area Problems Quiz

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Questions and Answers

What happens to the area of a rectangle when its length and width are both decreased by 2 cm?

  • The area doubles in size.
  • The area remains the same regardless of the decrease.
  • The area increases by a certain number of square centimeters.
  • The area decreases by 36 cm. (correct)

    • If a rectangle is originally twice as long as it is wide and each dimension is increased by 4 m, what will happen to its area?

  • The area becomes half of its original size.
  • The area increases by 88 m. (correct)
  • The area decreases significantly.
  • The area is unchanged.

    • What is the ratio of the length to the width for a rectangular swimming pool if it is three times as long as it is wide?

  • 3:1 (correct)
  • 2:3
  • 1:3
  • 1:2

    • What is the formula for the area of a semi-circle in terms of radius $r$?

    <p>$\frac{1}{2} \pi r^2$</p> Signup and view all the answers

    If the circumference of a circle is $2 \pi r$, what does $8r$ represent?

    <p>The distance around the outer edge of a different track</p> Signup and view all the answers

    How much area does the deck surrounding a swimming pool cover if the pool is 36 m by 12 m?

    <p>265 m</p> Signup and view all the answers

    If a poster is 25 cm taller than it is wide and has a border creating an area of 1350 cm for the border alone, what can be calculated?

    <p>The width of the poster.</p> Signup and view all the answers

    If one person stays 0.5 m from the inner edge of the track, what distance are they maintaining from the center of the track?

    <p>$r - 0.5$</p> Signup and view all the answers

    In a rectangular garden bordered by a patio, if the garden is 54 m in area and the patio is 1.5 m wide, what are the dimensions of the garden?

    <p>10 m by 5 m</p> Signup and view all the answers

    How much farther does a friend running outside the track run compared to someone running on the inner edge?

    <p>0.5 m</p> Signup and view all the answers

    If the circumference of a full circle is expressed as $2 \pi r$, what would be the total distance for one complete lap around a circuit of a track with a radius $r$?

    <p>$2 \pi r$</p> Signup and view all the answers

    What type of rooms does a house consist of if one room is square and the other is a rectangle that is 4 ft longer and 5 ft narrower than the square room?

    <p>One room is square, the other is more elongated.</p> Signup and view all the answers

    What is the relationship between the dimensions of a brick patio and its width when it is bordered by a garden that is 1.5 m wide?

    <p>The patio is wider than the garden.</p> Signup and view all the answers

    What is the relationship between the radius $r$ of the inner track and the outer track if the outer edge is 0.5 m farther?

    <p>$r_{outer} = r + 0.5$</p> Signup and view all the answers

    What does the variable $T$ likely represent in the context of running around a track?

    <p>Time taken</p> Signup and view all the answers

    Why might someone measure the distance from the outer edge of the track?

    <p>To ensure they run a specific distance</p> Signup and view all the answers

    What is the area of the lawn if the park is 5 m longer than it is wide, given that the area is 924 m²?

    <p>924 m²</p> Signup and view all the answers

    If a square lot originally measured x m on each side and lost 185 m² of area, which of the following represents the new area of the lot after widening by 3 m?

    <p>$x^2 - 185$</p> Signup and view all the answers

    Using the area formula $A = rac{22}{7}r^2$, find the area of a circle with a radius of 7 cm.

    <p>154 cm²</p> Signup and view all the answers

    If the radius of a circular pool is denoted as r, what is the relationship between the area of the walkway and the radius of the pool when the walkway is 3 m wide?

    <p>$198 = rac{22}{7}(r + 3)^2 - rac{22}{7}r^2$</p> Signup and view all the answers

    If the width of the shaded region surrounding a circle is 2 cm and the area is 76 cm², what is the radius of the circle?

    <p>13 cm</p> Signup and view all the answers

    What is the expected area of a running track that is 4 m wide surrounding a soccer field that is twice the inner radius r?

    <p>$2 rac{22}{7}r^2 + 32m^2$</p> Signup and view all the answers

    Which expression represents the new dimensions of the square lot after the adjacent streets are widened?

    <p>x - 3 by x + 3</p> Signup and view all the answers

    What is the significance of letting x represent the length of the original square lot?

    <p>It simplifies area calculations.</p> Signup and view all the answers

    Study Notes

    Rectangular Problems

    • A rectangle is three times as long as it is wide. Its length and width are both decreased by 2cm, and its area is decreased by 36cm².
      • Original dimensions: 15cm by 5cm
    • A rectangle is twice as long as it is wide. Both dimensions are increased by 4m, increasing its area by 88m².
      • Original dimensions: 12m by 6m

    Swimming Pool and Deck

    • A rectangular swimming pool is three times as long as it is wide, surrounded by a 2.5m wide deck. The deck's area is 265m².
      • Pool dimensions: 36m by 12m

    Poster and Cardboard

    • A poster is 25cm taller than it is wide. It's mounted with a 5cm border on all sides. The area of the border is 1350cm².
      • Poster dimensions: 50cm by 75cm

    Patio and Garden

    • A brick patio is twice as long as it is wide, surrounded by a 1.5m wide garden. The garden's area is 54m².
      • Patio dimensions: 10m by 5m

    Rooms of Equal Area

    • A house has two rooms of equal area. One is square, and the other is a rectangle 4ft narrower and 5ft longer than the square room.
      • Area of each room: 400ft²

    City Park

    • A small city park consists of a rectangular lawn surrounded by a 2.5m wide flower border. The park is 5 meters longer than wide.
      • Lawn area: 924m²

    Corner Lot

    • A square corner lot lost 185m² of area when one side was widened by 3m, and the other side was widened by 4m.
      • New dimensions: 20m by 22m

    Circle Area

    • Area of a circle: A = πr²
      • Formula for the shaded area of a circle with a rectangular segment removed: A = 2πr - (l x w)

    Circular Pool and Walkway

    • A circular pool is surrounded by a 3m wide brick walkway. The walkway's area is 198m².
      • Radius of the pool: 9m

    ### Running Track

    • A running track 4m wide surrounds a soccer field that is twice as long as wide. The track ends in semi-circles at each end.
      • Formula for the area of the track: Ar = 8πr + 16π

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    Algebra I 4.9 Answer Key PDF

    Description

    Test your skills with this quiz on rectangular problems involving dimensions, area changes, and related real-life scenarios. From swimming pools to posters, explore how to solve various geometric challenges. Perfect for students looking to strengthen their understanding of geometry.

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