**Areas of Parallelograms and Triangles**

To understand the concept of areas of parallelograms and triangles, let's break down the topic into two sections: areas of parallelograms and areas of triangles.

**Areas of Parallelograms:**

A parallelogram is a quadrilateral with opposite sides parallel. The formula to calculate the area of a parallelogram is given by:

Area = base × height

Here, the base refers to the length of any one of the parallel sides, and the height represents the perpendicular distance between the base and the opposite parallel side. To find the height, we can draw a perpendicular from any one of the vertices to the base, forming a right triangle. The length of this perpendicular is the height.

**Areas of Triangles:**

A triangle is a polygon with three sides. The formula to calculate the area of a triangle is given by:

Area = 1/2 × base × height

Here, the base refers to the length of any one of the sides, and the height represents the perpendicular distance between the base and the opposite vertex. Similar to the parallelogram, to find the height, we can draw a perpendicular from the vertex to the base, forming a right triangle. The length of this perpendicular is the height.

**Example:**

Let's consider an example to understand the application of these formulas. Suppose we have a parallelogram with a base length of 6 cm and a height of 4 cm. Using the formula for the area of a parallelogram, we can calculate:

Area = 6 cm × 4 cm = 24 cm²

Now, let's consider a triangle with a base length of 5 cm and a height of 8 cm. Using the formula for the area of a triangle, we can calculate:

Area = 1/2 × 5 cm × 8 cm = 20 cm²

**Conclusion:**

In conclusion, the area of a parallelogram is given by the formula Area = base × height, while the area of a triangle is given by the formula Area = 1/2 × base × height. These formulas help us calculate the amount of surface enclosed by these geometric shapes. By using the appropriate measurements for the base and height, we can easily determine the area of parallelograms and triangles.