To solve the problem, we need to find the perimeter and area of each shape. Let's tackle each part step by step.
Shape (1)
#### Perimeter
The shape is composed of two rectangles. To find the perimeter, we need to sum the lengths of all the outer edges.
- The top edge is 13 cm.
- The right edge is 9 cm.
- The bottom edge is 7 cm.
- The left edge is split into two parts: 5 cm (vertical) and 4 cm (horizontal).
Now, let's calculate the total perimeter:
\[
\text{Perimeter} = 13 + 9 + 7 + 5 + 4 + 4 = 42 \text{ cm}
\]
#### Area
The shape can be divided into two rectangles:
1. The larger rectangle has dimensions 13 cm by 9 cm.
2. The smaller rectangle has dimensions 5 cm by 4 cm.
The area of the larger rectangle is:
\[
13 \times 9 = 117 \text{ cm}^2
\]
The area of the smaller rectangle is:
\[
5 \times 4 = 20 \text{ cm}^2
\]
Since the smaller rectangle is part of the larger one, we do not need to subtract any overlapping area. The total area is simply the sum of the areas of the two rectangles:
\[
\text{Area} = 117 + 20 = 137 \text{ cm}^2
\]
Shape (2)
#### Perimeter
The shape is also composed of two rectangles. To find the perimeter, we need to sum the lengths of all the outer edges.
- The top edge is 5 cm.
- The right edge is 4 cm.
- The bottom edge is 9 cm.
- The left edge is split into two parts: 4 cm (vertical) and 5 cm (horizontal).
Now, let's calculate the total perimeter:
\[
\text{Perimeter} = 5 + 4 + 9 + 4 + 5 + 2 = 29 \text{ cm}
\]
#### Area
The shape can be divided into two rectangles:
1. The larger rectangle has dimensions 5 cm by 4 cm.
2. The smaller rectangle has dimensions 4 cm by 2 cm.
The area of the larger rectangle is:
\[
5 \times 4 = 20 \text{ cm}^2
\]
The area of the smaller rectangle is:
\[
4 \times 2 = 8 \text{ cm}^2
\]
Since the smaller rectangle is part of the larger one, we do not need to subtract any overlapping area. The total area is simply the sum of the areas of the two rectangles:
\[
\text{Area} = 20 + 8 = 28 \text{ cm}^2
\]
Final Answers
For Shape (1):
\[
\text{Perimeter} = 42 \text{ cm}, \quad \text{Area} = 137 \text{ cm}^2
\]
For Shape (2):
\[
\text{Perimeter} = 29 \text{ cm}, \quad \text{Area} = 28 \text{ cm}^2
\]
Putting the final answers in a box:
\[
\boxed{42 \text{ cm}, 137 \text{ cm}^2, 29 \text{ cm}, 28 \text{ cm}^2}
\]
Parent Tip: Review the logic above to help your child master the concept of area and perimeter of compound shapes worksheet.
