Question

goal
to be able to change between measures of area.
explore: finding conversion factors

1. a) a square foot measures one foot by one foot. in inches, what is the side length of a

square foot?
1 ft. = ____ in.
1 ft. = ____ in.
b) what is the area of the square in square inches? record your answer in the
conversion factor below.
1 square foot = ____________ square inches

1. a) a square metre measures one metre by one metre. in centimetres, what is the side

length of a square metre?
1 m = ____ cm
1 m = ____ cm
b) what is the area of the square in square centimeters? record your answer in the
conversion factor below.
1 m² = ____________ cm²

1. how many square feet, each measuring 1 foot by 1 foot, do you estimate it would

take to cover a square metre? record your answer in the conversion factor below.
1 m² = ____________ ft.²

Explanation:

Step1: Convert feet to inches

Since \(1\) foot \( = 12\) inches.

Step2: Calculate area in square inches

The area of a square with side length \(s\) is \(A=s^{2}\). For a square foot (\(s = 1\) foot \(=12\) inches), \(A=(12)^{2}=144\) square inches. So \(1\) square foot \(=144\) square inches.

Step3: Convert meters to centimeters

Since \(1\) meter \( = 100\) centimeters.

Step4: Calculate area in square centimeters

For a square meter (\(s = 1\) meter \(=100\) centimeters), \(A=(100)^{2}=10000\) square centimeters. So \(1m^{2}=10000cm^{2}\).

Step5: Convert square - meters to square - feet (approximate conversion)

We know that \(1\) meter \(=3.28084\) feet. Then for a square meter (\(s = 1\) meter \(=3.28084\) feet), \(A=(3.28084)^{2}\approx10.76\) square feet. So \(1m^{2}\approx10.76ft^{2}\)

Answer:

1. a) \(1\) ft. \(=12\) in. (both blanks)

b) \(1\) square foot \(=144\) square inches

1. a) \(1\) m \(=100\) cm (both blanks)

b) \(1m^{2}=10000cm^{2}\)

1. \(1m^{2}\approx10.76ft^{2}\)