https://file.aiquickdraw.com/mathbot/file/1726442400009nrqhnyj4.jpg

https://file.aiquickdraw.com/mathbot/file/1726442400011vtefkx3j.jpg

Find the area of each polygon. Write the name of the figure, the formula, the formula- and solve. Round to the nearest 100th and be sure to label your answer.

Let's go over each polygon one by one and calculate the area according to the given information.

### First Image

#### 1. Trapezoid
- **Base 1:** 17 yd
- **Base 2:** 6 yd
- **Height:** 16.1 yd
- **Formula:** 
  \[
  A = \frac{1}{2} \times (b_1 + b_2) \times h
  \]
  where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides and \( h \) is the height.
  
#### 2. Triangle
- **Base:** 35 in
- **Height:** 17.1 in
- **Formula:**
  \[
  A = \frac{1}{2} \times b \times h
  \]
  where \( b \) is the base and \( h \) is the height.

#### 3. Trapezoid
- **Base 1:** 12 yd
- **Base 2:** 6 yd
- **Height:** 8.8 yd
- **Formula:**
  \[
  A = \frac{1}{2} \times (b_1 + b_2) \times h
  \]

#### 4. Rectangle
- **Length:** 48 ft
- **Width:** 40 ft
- **Formula:**
  \[
  A = l \times w
  \]
  where \( l \) is the length and \( w \) is the width.

#### 5. Square
- **Side:** 10 in
- **Formula:**
  \[
  A = s^2
  \]
  where \( s \) is the length of the side.

#### 6. Rhombus
- **Diagonal 1 (PR):** 16 yd
- **Diagonal 2 (QS):** 10 yd
- **Formula:**
  \[
  A = \frac{1}{2} \times d_1 \times d_2
  \]
  where \( d_1 \) and \( d_2 \) are the diagonals.

---

### Second Image

#### 1. Rhombus
- **Diagonal 1 (PR):** 11 in
- **Diagonal 2 (SQ):** 24 in
- **Formula:**
  \[
  A = \frac{1}{2} \times d_1 \times d_2
  \]

#### 2. Rhombus
- **Diagonal 1:** 45 cm
- **Diagonal 2:** 63 cm
- **Formula:**
  \[
  A = \frac{1}{2} \times d_1 \times d_2
  \]

#### 3. Trapezoid
- **Base 1:** 23 in
- **Base 2:** 46 in
- **Height:** 32 in
- **Formula:**
  \[
  A = \frac{1}{2} \times (b_1 + b_2) \times h
  \]

#### 4. Right Triangle
- **Base:** 4 in
- **Height:** 4 in
- **Formula:**
  \[
  A = \frac{1}{2} \times b \times h
  \]

#### 5. Triangle
- **Base:** 33 cm
- **Height:** 16 cm
- **Formula:**
  \[
  A = \frac{1}{2} \times b \times h
  \]

#### 6. Trapezoid
- **Base 1:** 7 ft
- **Base 2:** 9 ft
- **Height:** 3 ft
- **Formula:**
  \[
  A = \frac{1}{2} \times (b_1 + b_2) \times h
  \]

---

I will now calculate the areas based on these formulas and dimensions. Let me perform the calculations.Here are the areas of each polygon from both images:

### First Image:
1. **Trapezoid**: 185.15 square yards
2. **Triangle**: 299.25 square inches
3. **Trapezoid**: 79.20 square yards
4. **Rectangle**: 1920 square feet
5. **Square**: 100 square inches
6. **Rhombus**: 80 square yards

### Second Image:
1. **Rhombus**: 132 square inches
2. **Rhombus**: 1417.5 square centimeters
3. **Trapezoid**: 1104 square inches
4. **Right Triangle**: 8 square inches
5. **Triangle**: 264 square centimeters
6. **Trapezoid**: 24 square feet

Let me know if you'd like any further clarification or detailed explanations!

---

Would you like to know more details about any of the calculations? Here are 5 follow-up questions to expand your understanding:
1. How do you calculate the area of a trapezoid with uneven base lengths?
2. Why is the formula for a rhombus based on its diagonals rather than its sides?
3. What would be the area if the measurements were converted to different units?
4. How can we derive the formula for the area of a triangle?
5. What are other common ways to find the area of irregular polygons?

**Tip:** Always ensure that units of measure are consistent when calculating areas. Converting to the same units before calculating helps avoid mistakes.

Find the area of each polygon. Write the name of the figure, the formula, and solve. Round to the nearest 100th and be sure to label your answer.

Learn how to find the area of polygons like trapezoids, triangles, rectangles, squares, and rhombuses. This exercise provides step-by-step solutions and formulas for calculating areas, ideal for students in Grades 8-10.

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