About Trapezoid Area Calculation

What is a Trapezoid?

A trapezoid (also known as a trapezium in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases, and the other two sides are called the legs.

Formula for Trapezoid Area

The formula to calculate the area of a trapezoid is:

\[A = \frac{1}{2}(a + b)h\]

Where:

• \(A\) is the area of the trapezoid
• \(a\) is the length of one parallel side (base)
• \(b\) is the length of the other parallel side (base)
• \(h\) is the height (perpendicular distance between the parallel sides)

Calculation Steps

1. Identify the lengths of the two parallel sides (bases).
2. Measure the height of the trapezoid (perpendicular to the bases).
3. Add the lengths of the two parallel sides.
4. Multiply the sum by the height.
5. Divide the result by 2 to get the area.

Example

Let's calculate the area of a trapezoid with bases 6 units and 10 units, and a height of 4 units:

1. Given:
   • Base 1 (\(a\)) = 6 units
   • Base 2 (\(b\)) = 10 units
   • Height (\(h\)) = 4 units
2. Apply the formula: \(A = \frac{1}{2}(a + b)h\)
3. Substitute the values: \(A = \frac{1}{2}(6 + 10) \times 4\)
4. Calculate:
   \(A = \frac{1}{2}(16) \times 4\)
   \(A = 8 \times 4\)
   \(A = 32\) square units

Visual representation:

Therefore, the area of the trapezoid is 32 square units.