Alexis has a rectangular piece of red paper that is 4 cm wide. Its length is twice its width. She glues a rectangular piece of blue paper on top of the red piece measuring 3 cm by 7 cm. How many sq cm of red paper will be visible on top
The Correct Answer and Explanation is:
Step 1: Finding the Area of the Red Paper
The red paper is rectangular with:
- Width = 4 cm
- Length = twice the width → 2 × 4 = 8 cm
So, its area is:
Area=Width×Length=4×8=32 cm2\text{Area} = \text{Width} \times \text{Length} = 4 \times 8 = 32 \text{ cm}^2
Step 2: Finding the Area of the Blue Paper
The blue paper has:
- Width = 3 cm
- Length = 7 cm
Thus, its area is:
Area=3×7=21 cm2\text{Area} = 3 \times 7 = 21 \text{ cm}^2
Step 3: Finding the Remaining Visible Red Paper
Since the blue paper is glued on top of the red paper, the remaining visible red paper is:
Visible Red Paper=Total Red Area−Covered Area\text{Visible Red Paper} = \text{Total Red Area} – \text{Covered Area}
=32−21=11 cm2= 32 – 21 = 11 \text{ cm}^2
Explanation:
This problem is a straightforward application of area subtraction. The red paper starts with 32 cm² of total space, but when a blue 21 cm² rectangular sheet is placed on top, it obscures part of the red surface. What remains visible is simply the difference between the areas.
One way to visualize this is by imagining the red rectangle as a desk and the blue rectangle as a paper placed on it—the leftover space around the edges is what remains visible.
Thus, Alexis will still see 11 cm² of red paper around the blue piece.
