A set of four stars form the shape of a rectangle in space. The length of the rectangle is approximately 5,360,000,000 miles, while the width of the rectangle is approximately 4,050,000,000 miles. What is the approximate area of the rectangle?

1 answer

To find the area of a rectangle, you can use the formula:

\[ \text{Area} = \text{Length} \times \text{Width} \]

For the rectangle described in the problem, the length is approximately 5,360,000,000 miles and the width is approximately 4,050,000,000 miles.

Plugging the numbers into the formula gives:

\[ \text{Area} = 5,360,000,000 , \text{miles} \times 4,050,000,000 , \text{miles} \]

To simplify the multiplication, we can first convert the numbers into scientific notation:

  • \( 5,360,000,000 \) can be written as \( 5.36 \times 10^9 \)
  • \( 4,050,000,000 \) can be written as \( 4.05 \times 10^9 \)

Now, we can multiply these two numbers:

\[ \text{Area} = (5.36 \times 10^9) \times (4.05 \times 10^9) \]

Using the properties of exponents, we can multiply the coefficients and add the exponents:

\[ \text{Area} = (5.36 \times 4.05) \times (10^9 \times 10^9) \]

Calculating \( 5.36 \times 4.05 \):

\[ 5.36 \times 4.05 \approx 21.658 \]

Calculating \( 10^9 \times 10^9 \):

\[ 10^9 \times 10^9 = 10^{18} \]

Putting it all together, we have:

\[ \text{Area} \approx 21.658 \times 10^{18} , \text{square miles} \]

For a more concise answer, we can express this in standard form:

\[ \text{Area} \approx 2.1658 \times 10^{19} , \text{square miles} \]

So the approximate area of the rectangle is:

\[ \text{Area} \approx 2.17 \times 10^{19} , \text{square miles} \]