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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?
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?
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?
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 $r$?
What is the formula for the area of a semi-circle in terms of radius $r$?
If the circumference of a circle is $2 \pi r$, what does $8r$ represent?
If the circumference of a circle is $2 \pi r$, what does $8r$ represent?
How much area does the deck surrounding a swimming pool cover if the pool is 36 m by 12 m?
How much area does the deck surrounding a swimming pool cover if the pool is 36 m by 12 m?
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?
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?
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?
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?
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?
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?
How much farther does a friend running outside the track run compared to someone running on the inner edge?
How much farther does a friend running outside the track run compared to someone running on the inner edge?
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 $r$?
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 $r$?
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?
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?
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?
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?
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?
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?
What does the variable $T$ likely represent in the context of running around a track?
What does the variable $T$ likely represent in the context of running around a track?
Why might someone measure the distance from the outer edge of the track?
Why might someone measure the distance from the outer edge of the track?
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?
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?
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?
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?
Using the area formula $A = rac{22}{7}r^2$, find the area of a circle with a radius of 7 cm.
Using the area formula $A = rac{22}{7}r^2$, find the area of a circle with a radius of 7 cm.
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?
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?
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?
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?
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?
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?
Which expression represents the new dimensions of the square lot after the adjacent streets are widened?
Which expression represents the new dimensions of the square lot after the adjacent streets are widened?
What is the significance of letting x represent the length of the original square lot?
What is the significance of letting x represent the length of the original square lot?
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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 = 2Ï€r - (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
###Â 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 = 8Ï€r + 16Ï€
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