Solved Examples and Worksheet for Area and Volume Measures using Scale Factors

Q1A parking lot is in the shape of a square measuring 19 ft by 12 ft. If you extend it by a scale factor of 3.5, find the new area of the parking lot.
A. 228 ft2
B. 235 ft2
C. 798 ft2
D. 2793 ft2

Solutions
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Step: 1
New area of the parking lot = Area of the original parking lot × (scale factor)2
  [Increasing the length of a side of an object by factor x increases the area by factor x2 .]
Step: 2
= (19 × 12) × (3.5)2
Step: 3
= 2793 ft2
Step: 4
Therefore, the new area of the parking lot is 2793 ft2.
Correct Answer is :   2793 ft2
Q2A lawn is in the shape of a rectangle measuring 12 ft by 7 ft. If you extend the lawn by a scale factor of 2, what will be the new area of the lawn?

A. 336 ft2
B. 320 ft2
C. 340 ft2
D. 200 ft2

Solutions
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Q3A park is in the shape of a square measuring 16 ft by 16 ft. If you extend the lawn by a scale factor of 4, what will be the new area of the park?

A. 3096 ft2
B. 4096 ft2
C. 3960 ft2
D. 4906 ft2

Solutions
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Q4A lawn is in the shape of a rectangle measuring 17 ft by 15 ft. If you extend it by a scale factor of 3, find the new area of the lawn.

A. 2095 ft2
B. 495 ft2
C. 2295 ft2
D. 1295 ft2

Solutions
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Step: 1
New area of the lawn = Area of the original lawn × (scale factor)2
  [Increasing the length of a side of an object by factor x increases the area by factor x2 .]
Step: 2
= (17 × 15) × (3)2
Step: 3
= 2295 ft2
Step: 4
Therefore, the new area of the lawn is 2295 ft2.
Correct Answer is :   2295 ft2
Q5A ground is in the shape of a square measuring 15 ft by 15 ft. If you extend it by a scale factor of 4, find the new area of the ground.

A. 4805 ft2
B. 3800 ft2
C. 3600 ft2
D. 1800 ft2

Solutions
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Step: 1
New area of the ground = Area of the original ground × (scale factor)2
  [Increasing the length of a side of an object by factor x increases the area by factor x2 .]
Step: 2
= (15 × 15) × (4)2
Step: 3
= 3600 ft2
Step: 4
Therefore, the new area of the ground is 3600 ft2.
Correct Answer is :   3600 ft2
Q6A field is in the shape of a rectangle measuring 24 ft by 18 ft. If you extend it by a scale factor of 2.5, find the new area of the field.

A. 2856 ft2
B. 2700 ft2
C. 1700 ft2
D. 2568 ft2

Solutions
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Step: 1
New area of the field = Area of the original field × (scale factor)2
  [Increasing the length of a side of an object by factor x increases the area by factor x2 .]
Step: 2
= (24 × 18) × (2.5)2
Step: 3
= 2700 ft2
Step: 4
Therefore, the new area of the field is 2700 ft2.
Correct Answer is :   2700 ft2
Q7In the figure, the bigger circle is the image of the smaller circle under an enlargement with centre O and scale factor 4. Given that the area of the larger circle is 80 cm2. Calculate the area of the smaller circle.

A. 5 cm2
B. 20 cm2
C. 320 cm2
D. 1280 cm2

Solutions
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Step: 1
Area of the larger circle = 80 cm2
Scale factor of the enlargement, k = 4
Step: 2
Area of object = Area of image ÷ k2
Step: 3
Area of the smaller circle = Area of the larger circle ÷ k2
Step: 4
= 80 ÷ 42
  [Substitute the values.]
Step: 5
= 80 ÷ 16
= 5
  [Divide.]
Step: 6
Therefore, the area of the smaller circle is 5 cm2.
Correct Answer is :   5 cm2
Q8In the figure, a circular garden of area 20 cm2 is enlarged by a scale of 3.5, with centre of enlargement O. Calculate the area of the shaded region.


A. 90 cm2
B. 265 cm2
C. 225 cm2
D. 50 cm2

Solutions
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Step: 1
Area of the circular garden = 20 cm2
Step: 2
Scale factor of the enlargement, k = 3.5
Step: 3
Area of image = k2 × Area of the object
Step: 4
Area of the enlarged garden = Area of the original garden × k2
Step: 5
= 20 × 3.52
  [Substitute the values.]
Step: 6
= 20 × 12.25
= 245cm2
  [Multiply.]
Step: 7
Area of the shaded region = Area of the enlarged garden - Area of the original garden
Step: 8
= 245 - 20
= 225
  [Substitute the values and subtract.]
Step: 9
Therefore, the area of the shaded region is 225 cm2.
Correct Answer is :   225 cm2

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