Question

name - 5th grade

1. a student draws a rectangle with a length of \\( \frac{3}{4} \\) foot and a width of \\( \frac{3}{4} \\) foot.

image of a 1 foot by 1 foot square divided into parts, with shaded area representing the rectangle
what is the area of the student’s rectangle?
a \\( \frac{1}{9} \\) foot
b \\( \frac{9}{16} \\) foot
c 3 foot
d 6 foot

Explanation:

Answer:

To find the area of a rectangle, we use the formula \( A = \text{length} \times \text{width} \).

Step 1: Identify the length and width

The length of the rectangle is \( \frac{3}{4} \) feet, and the width is also \( \frac{3}{4} \) feet.

Step 2: Multiply the length and width

Using the formula for the area of a rectangle:

$$ A = \frac{3}{4} \times \frac{3}{4} $$

When multiplying fractions, we multiply the numerators together and the denominators together:

$$ A = \frac{3 \times 3}{4 \times 4} = \frac{9}{16} $$

Wait, looking back at the options, maybe there was a typo in the problem (e.g., length and width might be \( \frac{3}{4} \) and \( \frac{2}{4} \) or similar). Assuming the intended length and width are \( \frac{3}{4} \) and \( \frac{2}{4} \) (or another combination), but based on the original problem as stated (length \( \frac{3}{4} \), width \( \frac{3}{4} \)), the area is \( \frac{9}{16} \). However, if the width was \( \frac{2}{4} \) (simplified to \( \frac{1}{2} \)):

Step 1: Correct length and width (assuming a typo)

If length \( = \frac{3}{4} \) and width \( = \frac{2}{4} = \frac{1}{2} \):

Step 2: Multiply

$$ A = \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8} $$

But since the options include \( \frac{9}{16} \) (if that’s an option) or other values, let’s re-examine the problem. The image shows a 1-foot by 1-foot square divided into 4 columns and 4 rows (16 small squares). The shaded rectangle has length \( \frac{3}{4} \) (3 columns) and width \( \frac{3}{4} \) (3 rows). So the number of shaded squares is \( 3 \times 3 = 9 \), and each square is \( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \) square feet. Thus, total area is \( 9 \times \frac{1}{16} = \frac{9}{16} \) square feet.

If the options include \( \frac{9}{16} \) (e.g., option B is \( \frac{9}{16} \)), then the answer is \( \frac{9}{16} \) square feet, corresponding to option B.