Here are the step-by-step solutions for the three problems on your worksheet.
Problem 1: Find the area of the shaded region (Grid)
Step 1: Understand the grid.
The problem states that each small square is $1 \text{ cm} \times 1 \text{ cm}$. This means the area of one single square is $1 \text{ cm}^2$.
Step 2: Count the squares.
We need to count how many pink squares make up the shape. Let's break it down by columns (vertical lines) from left to right:
*
Column 1: There are 4 squares.
*
Column 2: There are 4 squares.
*
Column 3: There are 2 squares.
*
Column 4: There are 2 squares.
*
Column 5: There are 2 squares.
Step 3: Add them up.
$$4 + 4 + 2 + 2 + 2 = 14$$
So, there are 14 squares in total. Since each square is $1 \text{ cm}^2$, the total area is $14 \text{ cm}^2$.
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Problem 2: Find the total area of the L-shaped cardboard
To find the area of an L-shape, we can split it into two separate rectangles, calculate their areas, and add them together. Let's split the shape vertically into a tall rectangle on the left and a shorter rectangle on the right.
Step 1: Identify the dimensions of the Left Rectangle.
* Looking at the diagram, the height of the left side is given as
$9 \text{ cm}$.
* We need to find the width of this left part. The total width at the bottom is $10 \text{ cm}$. The width of the right part is labeled as $8 \text{ cm}$.
* $\text{Width of Left Part} = \text{Total Width} - \text{Right Width}$
* $\text{Width} = 10 \text{ cm} - 8 \text{ cm} = \mathbf{2 \text{ cm}}$
*
Area of Left Rectangle = $\text{Height} \times \text{Width} = 9 \text{ cm} \times 2 \text{ cm} = \mathbf{18 \text{ cm}^2}$
Step 2: Identify the dimensions of the Right Rectangle.
* The width is given as
$8 \text{ cm}$.
* The height of this short section is given on the far right as
$3 \text{ cm}$.
*
Area of Right Rectangle = $\text{Height} \times \text{Width} = 3 \text{ cm} \times 8 \text{ cm} = \mathbf{24 \text{ cm}^2}$
Step 3: Add the areas together.
$$\text{Total Area} = 18 \text{ cm}^2 + 24 \text{ cm}^2 = 42 \text{ cm}^2$$
*(Self-Check using a different method: Imagine a big box $10 \times 9$ and subtract the empty space. Big Box Area = $90$. Empty space width is $8$, height is $9-3=6$. Empty Area = $48$. $90 - 48 = 42$. The answer matches.)*
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Problem 3: Find the area of the shaded region (Frame)
This shape is a large square with a smaller square hole cut out of the middle. To find the shaded area, we subtract the area of the hole from the area of the big square.
Step 1: Find the area of the Large Outer Square.
* The side length is given as
$6 \text{ cm}$.
* $\text{Area} = \text{side} \times \text{side} = 6 \text{ cm} \times 6 \text{ cm} = \mathbf{36 \text{ cm}^2}$
Step 2: Find the area of the Small Inner Square (the hole).
* The side length is given as
$2 \text{ cm}$.
* $\text{Area} = \text{side} \times \text{side} = 2 \text{ cm} \times 2 \text{ cm} = \mathbf{4 \text{ cm}^2}$
Step 3: Subtract the inner area from the outer area.
$$\text{Shaded Area} = 36 \text{ cm}^2 - 4 \text{ cm}^2 = 32 \text{ cm}^2$$
Final Answer:
1. 14 cm²
2. 42 cm²
3. 32 cm²
Parent Tip: Review the logic above to help your child master the concept of finding area of composite figures worksheet.
