A = (a+b)h/2

Definition

The formula A = (a+b)h/2 is used to calculate the area of a trapezoid, where 'a' and 'b' represent the lengths of the parallel bases, and 'h' represents the height or perpendicular distance between the bases. This formula is an important tool for understanding and applying the properties of rectangles, triangles, and trapezoids.

5 Must Know Facts For Your Next Test

1. The formula A = (a+b)h/2 is used to calculate the area of a trapezoid, which is a four-sided polygon with two parallel sides.
2. The 'a' and 'b' variables in the formula represent the lengths of the parallel bases of the trapezoid, while 'h' represents the height or perpendicular distance between the bases.
3. The formula is derived from the concept that the area of a trapezoid can be calculated as the average of the lengths of the parallel bases multiplied by the height.
4. Understanding this formula is crucial for solving problems related to the properties of rectangles, triangles, and trapezoids, as these shapes are often used in real-world applications.
5. Applying the A = (a+b)h/2 formula correctly is essential for accurately calculating the area of a trapezoid and understanding its relationship to other geometric shapes.

Review Questions

• Explain how the A = (a+b)h/2 formula is used to calculate the area of a trapezoid.
  • The A = (a+b)h/2 formula is used to calculate the area of a trapezoid by taking the average of the lengths of the parallel bases ('a' and 'b') and multiplying it by the height ('h') of the trapezoid. This formula is derived from the concept that the area of a trapezoid can be calculated as the sum of the areas of two triangles formed by the parallel bases and the height. By using this formula, you can easily determine the area of a trapezoid given the lengths of the parallel bases and the height.
• Describe how the A = (a+b)h/2 formula is related to the properties of rectangles, triangles, and trapezoids.
  • The A = (a+b)h/2 formula is closely related to the properties of rectangles, triangles, and trapezoids. For a rectangle, where the parallel bases are equal in length (a = b), the formula simplifies to A = bh, which is the standard formula for the area of a rectangle. For a triangle, where one of the parallel bases is zero (a or b = 0), the formula reduces to A = 1/2 * b * h, which is the area formula for a triangle. The A = (a+b)h/2 formula is specifically designed for trapezoids, which have two parallel bases of different lengths, and it allows for the calculation of the area of this unique four-sided polygon.
• Analyze how the variables in the A = (a+b)h/2 formula (a, b, and h) influence the area of a trapezoid, and explain the significance of each variable.
  • The variables in the A = (a+b)h/2 formula (a, b, and h) all play a crucial role in determining the area of a trapezoid. The 'a' and 'b' variables represent the lengths of the parallel bases, and as these values increase, the area of the trapezoid will also increase, assuming the height 'h' remains constant. The 'h' variable represents the height or perpendicular distance between the parallel bases, and as this value increases, the area of the trapezoid will also increase, assuming the base lengths 'a' and 'b' remain constant. The significance of each variable lies in the fact that they collectively define the unique shape and size of the trapezoid, and by understanding how changes in these variables affect the area, you can effectively solve problems related to the properties of trapezoids and other related geometric shapes.

Related terms

Trapezoid:

A quadrilateral with two parallel sides of different lengths.

Parallel Bases: The two opposite sides of a trapezoid that are parallel to each other.

Height:

The perpendicular distance between the parallel bases of a trapezoid.