https://file.aiquickdraw.com/mathbot/file/1725872272620zky5ymww.jpg

Let's go through the problems in the image and solve them step by step.

### Problem 1
We are tasked with finding the areas of the composite shapes shown. Each shape is made up of rectangles, and we can calculate the total area by summing the areas of these rectangles.

#### a. 
- The shape is made of two rectangles:
  - Large rectangle: 4 cm by 4 cm
  - Small rectangle: 2 cm by 2 cm
- **Total Area**: $ A = 4 \times 4 + 2 \times 2 = 16 + 4 = 20 \, \text{cm}^2 $

#### b. 
- The shape is made of two rectangles:
  - Horizontal rectangle: 2 cm by 20 cm
  - Vertical rectangle: 1.5 cm by 5 cm
- **Total Area**: $ A = 2 \times 20 + 1.5 \times 5 = 40 + 7.5 = 47.5 \, \text{cm}^2 $

### Problem 2
We need to find the area of composite shapes by first finding the areas of the smaller rectangles.

#### a. 
- The shape is made of four rectangles of equal dimensions:
  - Each rectangle is 3.5 m by 2 m
- **Total Area**: $ A = 4 \times (3.5 \times 2) = 4 \times 7 = 28 \, \text{m}^2 $

#### b. 
- The shape is made of a square and a triangle:
  - Square: 12 cm by 12 cm
  - Triangle (base = 5 m, height = 2 m):
    - Area of triangle: $ \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 2 = 5 \, \text{m}^2 $
- **Total Area**: $ A = 12 \times 12 + 5 = 144 + 5 = 149 \, \text{cm}^2 $

#### c. 
- A right triangle with base = 5 m and height = 2 m.
- **Total Area**: $ A = \frac{1}{2} \times 5 \times 2 = 5 \, \text{m}^2 $

#### d. 
- The shape is made of three rectangles:
  - Large rectangle: 2 cm by 6 cm
  - Two small rectangles: 2 cm by 1 cm and 1 cm by 3.5 cm
- **Total Area**: $ A = (2 \times 6) + (2 \times 1) + (1 \times 3.5) = 12 + 2 + 3.5 = 17.5 \, \text{cm}^2 $

### Problem 6
This problem involves finding the area of a wall after subtracting the area of the three square holes.
- Wall dimensions: 5 m by 2.4 m
- Each square hole: 1.2 m by 1.2 m
- Total area of the wall: $ A_{\text{wall}} = 5 \times 2.4 = 12 \, \text{m}^2 $
- Area of three square holes: $ 3 \times (1.2 \times 1.2) = 3 \times 1.44 = 4.32 \, \text{m}^2 $
- **Remaining area**: $ A = 12 - 4.32 = 7.68 \, \text{m}^2 $

### Problem 7
We are tasked with calculating the cost of covering a factory floor with linoleum.
- Floor dimensions: 12 m by 10 m minus a cut-out area of 5 m by 4 m
- Area to cover: $ A = (12 \times 10) - (5 \times 4) = 120 - 20 = 100 \, \text{m}^2 $
- Linoleum cost: $25 per square meter
- Total cost: $ 100 \times 25 = 2500 $
- Budget: $3000
- **Conclusion**: Yes, there is enough money in the budget to cover the cost.

---

Do you want further details or clarifications on any specific part? 

Here are 5 related questions you might find helpful:
1. How do you calculate the area of irregular composite shapes?
2. What is the formula for calculating the area of a triangle?
3. How do you convert between square meters and square centimeters?
4. How can you estimate material costs for large-scale projects?
5. What other methods can be used to simplify composite area problems?

**Tip**: For composite shapes, always break them down into basic geometric shapes and calculate their areas separately.

Solve the composite area problems, calculate the remaining area of a wall with square holes, and determine the cost of covering a factory floor with linoleum.

Learn how to calculate the area of composite shapes, determine the remaining area of a wall after cutting out square holes, and estimate the cost of covering a factory floor with linoleum. This lesson covers key geometric concepts such as area of rectangles, triangles, and cost estimation. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation