Find the area of the triangle defined by the points and .
9
16
18
4.5

QUESTION 3

Which shapes have the same area?

II.
III.
They all have different areas
II and III
I, II and III
I and II

Ask by Fernandez Norton. in the United States

Jan 24,2025

Question

Find the area of the triangle defined by the points and .
9
16
18
4.5

QUESTION 3

Which shapes have the same area?

II.
III.
They all have different areas
II and III
I, II and III
I and II

Ask by Fernandez Norton. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

Let's address each question one by one.

---

### **Question 2**

**Find the area of the triangle defined by the points $$ (2,3), (-4,3) $$, and $$ (-6,6) $$.**

**Options:**
- 9
- 16
- 18
- 4.5

**Solution:**

1. **Identify the Base and Height:**
   - Points $$ A(2,3) $$ and $$ B(-4,3) $$ lie on the same horizontal line ($$ y = 3 $$), so $$ AB $$ can serve as the base.
   - Length of base $$ AB $$:
     $$
     |2 - (-4)| = 6 \text{ units}
     $$
   - The height is the vertical distance from point $$ C(-6,6) $$ to the line $$ y = 3 $$:
     $$
     6 - 3 = 3 \text{ units}
     $$

2. **Calculate the Area:**
   $$
   \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 3 = 9
   $$

**Answer:** **9**

---

### **Question 3**

**Which shapes have the same area?**

**Given Shapes:**
1. **I.** Points $$ (1,1), (1,4), (4,4), (4,1) $$
2. **II.** Points $$ (0,0), (0,-4.5), (-2,0), (-2,-4.5) $$
3. **III.** Points $$ (4,-3), (2,-5), (6,-5) $$

**Options:**
- They all have different areas
- II and III
- I, II and III
- I and II

**Solution:**

1. **Shape I:**
   - This is a rectangle with length and width both equal to 3 units.
   - **Area:** $$ 3 \times 3 = 9 $$

2. **Shape II:**
   - This is a rectangle with length 2 units and height 4.5 units.
   - **Area:** $$ 2 \times 4.5 = 9 $$

3. **Shape III:**
   - This is a triangle with a base of 4 units and a height of 2 units.
   - **Area:** $$ \frac{1}{2} \times 4 \times 2 = 4 $$

**Conclusion:**
- Shapes **I** and **II** both have an area of **9**.
- Shape **III** has a different area of **4**.

**Answer:** **I and II**

---
**Question 2:** The area of the triangle is **9**. **Question 3:** Shapes **I** and **II** have the same area.

Find the area of the triangle defined by the points and .
9
16
18
4.5

QUESTION 3

Which shapes have the same area?

II.
III.
They all have different areas
II and III
I, II and III
I and II

Upstudy AI Solution

Answer

Solution

Question 2

Question 3

Bonus Knowledge

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Latest Geometry Questions

Find the area of the triangle defined by the points and . 9 16 18 4.5 QUESTION 3 Which shapes have the same area? II. III. They all have different areas II and III I, II and III I and II

Upstudy AI Solution

Answer

Solution

Question 2

Question 3

Bonus Knowledge

Related Questions

Latest Geometry Questions

Find the area of the triangle defined by the points and .
9
16
18
4.5

QUESTION 3

Which shapes have the same area?

II.
III.
They all have different areas
II and III
I, II and III
I and II