Problem Analysis:
The given composite figure consists of two rectangles connected side by side with a small gap in between. We are tasked with calculating both the
area and the
perimeter of this composite figure.
#### Given Dimensions:
- Left rectangle:
- Width = 15 mm
- Height = 15 mm (since it is a square)
- Right rectangle:
- Width = 10 mm
- Height = 10 mm (since it is a square)
- Gap between the rectangles:
- Width = 8 mm
- Total width of the composite figure:
- 30 mm
---
Step 1: Calculate the Area
The area of the composite figure is the sum of the areas of the two rectangles.
#### Area of the Left Rectangle:
\[
\text{Area}_{\text{left}} = \text{Width} \times \text{Height} = 15 \, \text{mm} \times 15 \, \text{mm} = 225 \, \text{mm}^2
\]
#### Area of the Right Rectangle:
\[
\text{Area}_{\text{right}} = \text{Width} \times \text{Height} = 10 \, \text{mm} \times 10 \, \text{mm} = 100 \, \text{mm}^2
\]
#### Total Area:
\[
\text{Total Area} = \text{Area}_{\text{left}} + \text{Area}_{\text{right}} = 225 \, \text{mm}^2 + 100 \, \text{mm}^2 = 325 \, \text{mm}^2
\]
---
Step 2: Calculate the Perimeter
The perimeter of the composite figure is the sum of all the outer edges. To calculate this, we need to consider the following:
1. The left rectangle contributes three sides to the perimeter (top, left, and bottom).
2. The right rectangle contributes three sides to the perimeter (top, right, and bottom).
3. The gap between the rectangles does not add any additional perimeter since it is an internal space.
#### Perimeter Calculation:
- Top edge:
\[
\text{Top edge} = 15 \, \text{mm} + 10 \, \text{mm} = 25 \, \text{mm}
\]
- Bottom edge:
\[
\text{Bottom edge} = 15 \, \text{mm} + 10 \, \text{mm} = 25 \, \text{mm}
\]
- Left edge (from the left rectangle):
\[
\text{Left edge} = 15 \, \text{mm}
\]
- Right edge (from the right rectangle):
\[
\text{Right edge} = 10 \, \text{mm}
\]
#### Total Perimeter:
\[
\text{Total Perimeter} = \text{Top edge} + \text{Bottom edge} + \text{Left edge} + \text{Right edge}
\]
\[
\text{Total Perimeter} = 25 \, \text{mm} + 25 \, \text{mm} + 15 \, \text{mm} + 10 \, \text{mm} = 75 \, \text{mm}
\]
---
Final Answers:
\[
\boxed{325 \, \text{mm}^2, 75 \, \text{mm}}
\]
Parent Tip: Review the logic above to help your child master the concept of perimeter and area of composite figures worksheet.
