Find the perimeter and area of the shaded figure below: Perimeter: 12 units Area: 8 square units
The Correct Answer and Explanation is:
The correct answer for the shaded figure in the image is:
- Area: 8 square units ✅
- Perimeter: 18 units ❌ (not 12 units as shown in the image)
📏 Explanation
To determine the area and perimeter of the shaded rectangle, we must examine the figure closely.
✅ Area
Area is calculated using the formula for the area of a rectangle: Area=Length×Width\text{Area} = \text{Length} \times \text{Width}
From the grid:
- The shaded figure spans 4 squares vertically (length).
- It spans 2 squares horizontally (width).
So, Area=4×2=8 square units\text{Area} = 4 \times 2 = 8 \text{ square units}
This confirms that the given area is correct.
❌ Perimeter
Perimeter is the total distance around the outside of the figure. For a rectangle: Perimeter=2×(Length+Width)\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
Using the same measurements:
- Length = 4 units
- Width = 2 units
Perimeter=2×(4+2)=2×6=12 units\text{Perimeter} = 2 \times (4 + 2) = 2 \times 6 = 12 \text{ units}
Wait—that suggests 12 units is correct. But let’s verify using the grid.
Looking carefully at the shaded figure:
- Height (vertical sides): 4 units (2 sides → 4 + 4 = 8)
- Width (horizontal sides): 1 unit (2 sides → 1 + 1 = 2)
There is an error in labeling. The rectangle is 4 units high and 1 unit wide, not 2 units wide. So the correct dimensions are:
- Length = 4 units
- Width = 1 unit
Now recalculate: Area=4×1=4 square units\text{Area} = 4 \times 1 = 4 \text{ square units} Perimeter=2×(4+1)=2×5=10 units\text{Perimeter} = 2 \times (4 + 1) = 2 \times 5 = 10 \text{ units}
But based on actual counting of grid squares, the shaded figure is 4 units high and 2 units wide, making:
- Area = 4 × 2 = 8 square units
- Perimeter = 2 × (4 + 2) = 12 units
So the original answer in the image is actually correct, and my initial correction was mistaken.
✅ Final Answer:
- Area: 8 square units
- Perimeter: 12 units
The original solution is correct after all!
