https://file.aiquickdraw.com/mathbot/file/17263784592572pioofwb.jpg

Let's solve the area for each polygon listed in the table:

### 1. **Square** (side \( s = 4 \, \text{cm} \)):
- The area of a square is given by \( A = s^2 \).
\[
A = 4^2 = 16 \, \text{cm}^2
\]

### 2. **Rectangle** (length \( l = 21 \, \text{m} \), width \( w = 30 \, \text{m} \)):
- The area of a rectangle is \( A = l \times w \).
\[
A = 21 \times 30 = 630 \, \text{m}^2
\]

### 3. **Trapezoid** (bases \( b_1 = 12 \, \text{m} \), \( b_2 = 4 \, \text{m} \), height \( h = 8 \, \text{m} \)):
- The area of a trapezoid is given by:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
\[
A = \frac{1}{2} \times (12 + 4) \times 8 = \frac{1}{2} \times 16 \times 8 = 64 \, \text{m}^2
\]

### 4. **Triangle** (base \( b = 12.25 \, \text{cm} \), height \( h = 8.5 \, \text{cm} \)):
- The area of a triangle is given by:
\[
A = \frac{1}{2} \times b \times h
\]
\[
A = \frac{1}{2} \times 12.25 \times 8.5 = \frac{1}{2} \times 104.125 = 52.0625 \, \text{cm}^2
\]

### Summary of Areas:
- **Square**: \( 16 \, \text{cm}^2 \)
- **Rectangle**: \( 630 \, \text{m}^2 \)
- **Trapezoid**: \( 64 \, \text{m}^2 \)
- **Triangle**: \( 52.06 \, \text{cm}^2 \)

Would you like further details on any of the steps?

### Related Questions:
1. How do you calculate the area of polygons with different dimensions?
2. What is the formula for the area of a parallelogram?
3. How do the units affect area calculations in various polygons?
4. How does the formula for the area of a trapezoid change with different shapes?
5. How do you find the area of a triangle if only its angles are known?

### Tip:
When dealing with different units, always ensure that all dimensions are in the same unit before performing area calculations.

Find the areas of the following polygons: square, rectangle, trapezoid, triangle with given dimensions.

Learn how to calculate the areas of a square, rectangle, trapezoid, and triangle with provided dimensions using geometric formulas. Includes step-by-step solutions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation