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: Find dimensions of the red paper
We are told:
- The red paper is 4 cm wide
- Its length is twice the width
So,
- Length = 2 × 4 = 8 cm
- Therefore, the area of the red paper is:
Areared=length×width=8×4=32 cm2\text{Area}_{\text{red}} = \text{length} \times \text{width} = 8 \times 4 = 32 \text{ cm}^2Areared=length×width=8×4=32 cm2
Step 2: Find area of the blue paper
We are told the blue paper measures:
- 3 cm by 7 cm
So, Areablue=3×7=21 cm2\text{Area}_{\text{blue}} = 3 \times 7 = 21 \text{ cm}^2Areablue=3×7=21 cm2
Step 3: Calculate the visible red area
Assuming the blue paper is fully on top of the red paper and does not hang over any edge, the blue paper hides 21 cm² of the red surface.
Thus, the visible red area is: Visible red area=Areared−Areablue=32−21=11 cm2\text{Visible red area} = \text{Area}_{\text{red}} – \text{Area}_{\text{blue}} = 32 – 21 = \boxed{11 \text{ cm}^2}Visible red area=Areared−Areablue=32−21=11 cm2
Explanation (300 words)
This problem involves basic geometry and understanding of area. Alexis starts with a red rectangular piece of paper with a width of 4 cm. Since the length is described as being “twice its width,” we multiply 4 cm by 2, giving us a length of 8 cm. This gives us a red rectangle of dimensions 4 cm by 8 cm.
To find the area of a rectangle, we use the formula: Area=Length×Width\text{Area} = \text{Length} \times \text{Width}Area=Length×Width
So the red paper’s area is: 8 cm×4 cm=32 cm28 \text{ cm} \times 4 \text{ cm} = 32 \text{ cm}^28 cm×4 cm=32 cm2
Next, we examine the blue paper, which is also a rectangle with dimensions 3 cm by 7 cm. Its area is: 3 cm×7 cm=21 cm23 \text{ cm} \times 7 \text{ cm} = 21 \text{ cm}^23 cm×7 cm=21 cm2
Now, since the blue paper is glued on top of the red one, it will cover part of it. Assuming the blue paper is fully contained within the red (which it is, because 3 cm < 4 cm and 7 cm < 8 cm), it covers exactly 21 cm² of the red paper.
To find how much red paper is still visible, we subtract the blue area from the red: 32−21=11 cm232 – 21 = 11 \text{ cm}^232−21=11 cm2
So, the amount of visible red paper left is 11 square centimeters. This is the final, correct answer.
✅ Final Answer: 11 cm²
