Area of Triangles Worksheet by Jessicas Corner of Cyberspace | TPT - Free Printable

To solve the problem, we need to calculate the area of each triangle using the formula for the area of a triangle:

\[
\text{Area of a Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]

Additionally, we will compare this with the area of the rectangle that encloses the triangle. The area of the rectangle is given by:

\[
\text{Area of Rectangle} = \text{Base} \times \text{Height}
\]

Let's go through each triangle step by step.

---

Triangle 1:

#### Step 1: Identify the Base and Height
- Base: The base of the triangle is the horizontal side at the bottom. From the grid, the base is 6 cm.
- Height: The height is the vertical distance from the base to the opposite vertex. From the grid, the height is 4 cm.

#### Step 2: Calculate the Area of the Rectangle
\[
\text{Rectangle Area} = \text{Base} \times \text{Height} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2
\]

#### Step 3: Calculate the Area of the Triangle
\[
\text{Triangle Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 6 \, \text{cm} \times 4 \, \text{cm} = 12 \, \text{cm}^2
\]

#### Final Answer for Triangle 1:
\[
\boxed{\text{Base: } 6 \, \text{cm}, \text{ Height: } 4 \, \text{cm}, \text{ Rectangle Area: } 24 \, \text{cm}^2, \text{ Triangle Area: } 12 \, \text{cm}^2}
\]

---

Triangle 2:

#### Step 1: Identify the Base and Height
- Base: The base of the triangle is the horizontal side at the bottom. From the grid, the base is 5 cm.
- Height: The height is the vertical distance from the base to the opposite vertex. From the grid, the height is 4 cm.

#### Step 2: Calculate the Area of the Rectangle
\[
\text{Rectangle Area} = \text{Base} \times \text{Height} = 5 \, \text{cm} \times 4 \, \text{cm} = 20 \, \text{cm}^2
\]

#### Step 3: Calculate the Area of the Triangle
\[
\text{Triangle Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = 10 \, \text{cm}^2
\]

#### Final Answer for Triangle 2:
\[
\boxed{\text{Base: } 5 \, \text{cm}, \text{ Height: } 4 \, \text{cm}, \text{ Rectangle Area: } 20 \, \text{cm}^2, \text{ Triangle Area: } 10 \, \text{cm}^2}
\]

---

Triangle 3:

#### Step 1: Identify the Base and Height
- Base: The base of the triangle is the horizontal side at the bottom. From the grid, the base is 7 cm.
- Height: The height is the vertical distance from the base to the opposite vertex. From the grid, the height is 3 cm.

#### Step 2: Calculate the Area of the Rectangle
\[
\text{Rectangle Area} = \text{Base} \times \text{Height} = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]

#### Step 3: Calculate the Area of the Triangle
\[
\text{Triangle Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 7 \, \text{cm} \times 3 \, \text{cm} = 10.5 \, \text{cm}^2
\]

#### Final Answer for Triangle 3:
\[
\boxed{\text{Base: } 7 \, \text{cm}, \text{ Height: } 3 \, \text{cm}, \text{ Rectangle Area: } 21 \, \text{cm}^2, \text{ Triangle Area: } 10.5 \, \text{cm}^2}
\]

---

Triangle 4:

#### Step 1: Identify the Base and Height
- Base: The base of the triangle is the horizontal side at the bottom. From the grid, the base is 8 cm.
- Height: The height is the vertical distance from the base to the opposite vertex. From the grid, the height is 3 cm.

#### Step 2: Calculate the Area of the Rectangle
\[
\text{Rectangle Area} = \text{Base} \times \text{Height} = 8 \, \text{cm} \times 3 \, \text{cm} = 24 \, \text{cm}^2
\]

#### Step 3: Calculate the Area of the Triangle
\[
\text{Triangle Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 8 \, \text{cm} \times 3 \, \text{cm} = 12 \, \text{cm}^2
\]

#### Final Answer for Triangle 4:
\[
\boxed{\text{Base: } 8 \, \text{cm}, \text{ Height: } 3 \, \text{cm}, \text{ Rectangle Area: } 24 \, \text{cm}^2, \text{ Triangle Area: } 12 \, \text{cm}^2}
\]

---

Summary of All Answers:

1. Triangle 1:
\[
\boxed{\text{Base: } 6 \, \text{cm}, \text{ Height: } 4 \, \text{cm}, \text{ Rectangle Area: } 24 \, \text{cm}^2, \text{ Triangle Area: } 12 \, \text{cm}^2}
\]

2. Triangle 2:
\[
\boxed{\text{Base: } 5 \, \text{cm}, \text{ Height: } 4 \, \text{cm}, \text{ Rectangle Area: } 20 \, \text{cm}^2, \text{ Triangle Area: } 10 \, \text{cm}^2}
\]

3. Triangle 3:
\[
\boxed{\text{Base: } 7 \, \text{cm}, \text{ Height: } 3 \, \text{cm}, \text{ Rectangle Area: } 21 \, \text{cm}^2, \text{ Triangle Area: } 10.5 \, \text{cm}^2}
\]

4. Triangle 4:
\[
\boxed{\text{Base: } 8 \, \text{cm}, \text{ Height: } 3 \, \text{cm}, \text{ Rectangle Area: } 24 \, \text{cm}^2, \text{ Triangle Area: } 12 \, \text{cm}^2}
\]