To solve the problem, we need to determine the area of the given shape. The shape appears to be composed of two rectangles that are connected at one corner. Let's break it down step by step.
Step 1: Identify the dimensions of the two rectangles
The shape can be divided into two rectangles:
1.
Top-left rectangle:
- Width = 3 cm
- Height = 5 cm
2.
Bottom-right rectangle:
- Width = 7 cm
- Height = 3 cm
Step 2: Calculate the area of each rectangle
The area of a rectangle is given by the formula:
\[
\text{Area} = \text{Width} \times \text{Height}
\]
#### Area of the top-left rectangle:
\[
\text{Area}_{\text{top-left}} = 3 \, \text{cm} \times 5 \, \text{cm} = 15 \, \text{cm}^2
\]
#### Area of the bottom-right rectangle:
\[
\text{Area}_{\text{bottom-right}} = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]
Step 3: Subtract the overlapping area
The two rectangles overlap in a small square at their connection point. To avoid double-counting this overlapping area, we need to subtract it once.
#### Dimensions of the overlapping square:
- The overlapping square has a side length of 2 cm (as indicated in the image).
#### Area of the overlapping square:
\[
\text{Area}_{\text{overlap}} = 2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2
\]
Step 4: Calculate the total area of the shape
The total area of the shape is the sum of the areas of the two rectangles minus the area of the overlapping square:
\[
\text{Total Area} = \text{Area}_{\text{top-left}} + \text{Area}_{\text{bottom-right}} - \text{Area}_{\text{overlap}}
\]
\[
\text{Total Area} = 15 \, \text{cm}^2 + 21 \, \text{cm}^2 - 4 \, \text{cm}^2 = 32 \, \text{cm}^2
\]
Final Answer:
\[
\boxed{32}
\]
Parent Tip: Review the logic above to help your child master the concept of area and perimeter of compound shapes worksheet.
