Area of Polygons Worksheets - Free Printable

To solve the problem of finding the area of each irregular polygon, we need to break down each shape into simpler geometric figures (such as triangles, rectangles, and trapezoids) whose areas can be calculated using standard formulas. Let's go through each polygon step by step.

---

Polygon 1:

The first polygon is composed of a rectangle and two right triangles.

#### Step 1: Identify the dimensions.
- The rectangle has a base of 8 units and a height of 4 units.
- The two right triangles have bases of 3 units each and heights of 4 units each.

#### Step 2: Calculate the area of the rectangle.
The formula for the area of a rectangle is:
\[
\text{Area}_{\text{rectangle}} = \text{base} \times \text{height}
\]
\[
\text{Area}_{\text{rectangle}} = 8 \times 4 = 32 \text{ square units}
\]

#### Step 3: Calculate the area of one right triangle.
The formula for the area of a triangle is:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For one triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 3 \times 4 = 6 \text{ square units}
\]

#### Step 4: Calculate the total area of the two triangles.
\[
\text{Total Area}_{\text{triangles}} = 2 \times 6 = 12 \text{ square units}
\]

#### Step 5: Calculate the total area of the polygon.
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Total Area}_{\text{triangles}}
\]
\[
\text{Total Area} = 32 + 12 = 44 \text{ square units}
\]

---

Polygon 2:

The second polygon is composed of a rectangle and two right triangles.

#### Step 1: Identify the dimensions.
- The rectangle has a base of 6 units and a height of 4 units.
- The two right triangles have bases of 2 units each and heights of 4 units each.

#### Step 2: Calculate the area of the rectangle.
\[
\text{Area}_{\text{rectangle}} = \text{base} \times \text{height}
\]
\[
\text{Area}_{\text{rectangle}} = 6 \times 4 = 24 \text{ square units}
\]

#### Step 3: Calculate the area of one right triangle.
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For one triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 2 \times 4 = 4 \text{ square units}
\]

#### Step 4: Calculate the total area of the two triangles.
\[
\text{Total Area}_{\text{triangles}} = 2 \times 4 = 8 \text{ square units}
\]

#### Step 5: Calculate the total area of the polygon.
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Total Area}_{\text{triangles}}
\]
\[
\text{Total Area} = 24 + 8 = 32 \text{ square units}
\]

---

Polygon 3:

The third polygon is composed of a parallelogram and a triangle.

#### Step 1: Identify the dimensions.
- The parallelogram has a base of 7 units and a height of 4 units.
- The triangle has a base of 3 units and a height of 4 units.

#### Step 2: Calculate the area of the parallelogram.
The formula for the area of a parallelogram is:
\[
\text{Area}_{\text{parallelogram}} = \text{base} \times \text{height}
\]
\[
\text{Area}_{\text{parallelogram}} = 7 \times 4 = 28 \text{ square units}
\]

#### Step 3: Calculate the area of the triangle.
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 3 \times 4 = 6 \text{ square units}
\]

#### Step 4: Calculate the total area of the polygon.
\[
\text{Total Area} = \text{Area}_{\text{parallelogram}} + \text{Area}_{\text{triangle}}
\]
\[
\text{Total Area} = 28 + 6 = 34 \text{ square units}
\]

---

Polygon 4:

The fourth polygon is composed of a rectangle and two right triangles.

#### Step 1: Identify the dimensions.
- The rectangle has a base of 6 units and a height of 4 units.
- The two right triangles have bases of 2 units each and heights of 4 units each.

#### Step 2: Calculate the area of the rectangle.
\[
\text{Area}_{\text{rectangle}} = \text{base} \times \text{height}
\]
\[
\text{Area}_{\text{rectangle}} = 6 \times 4 = 24 \text{ square units}
\]

#### Step 3: Calculate the area of one right triangle.
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For one triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 2 \times 4 = 4 \text{ square units}
\]

#### Step 4: Calculate the total area of the two triangles.
\[
\text{Total Area}_{\text{triangles}} = 2 \times 4 = 8 \text{ square units}
\]

#### Step 5: Calculate the total area of the polygon.
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Total Area}_{\text{triangles}}
\]
\[
\text{Total Area} = 24 + 8 = 32 \text{ square units}
\]

---

Final Answers:

\[
\boxed{44, 32, 34, 32}
\]