Altitude

Definition

Altitude is the vertical distance or height of an object above a reference level, such as sea level. It is a fundamental concept in geometry and is particularly important when studying the properties of rectangles, triangles, and trapezoids.

5 Must Know Facts For Your Next Test

1. The altitude of a rectangle is the perpendicular distance between the opposite sides, and it is used to calculate the area of the rectangle.
2. In a triangle, the altitude is the perpendicular distance from the base to the opposite vertex, and it is a key factor in determining the area of the triangle.
3. For a trapezoid, the altitude is the perpendicular distance between the two parallel bases, and it is used in the formula for calculating the area of the trapezoid.
4. The altitude of a shape is often denoted by the variable 'h' and is a crucial measurement in many geometric formulas and calculations.
5. Understanding the concept of altitude is essential for solving problems involving the properties and calculations of rectangles, triangles, and trapezoids.

Review Questions

• Explain how the altitude of a rectangle is used to calculate its area.
  • The area of a rectangle is calculated by multiplying its length and width. The altitude, or perpendicular height, of a rectangle is the distance between the opposite sides and is one of the dimensions used in the area formula. Specifically, the area of a rectangle is given by the formula $A = l \times h$, where $l$ is the length and $h$ is the altitude or height of the rectangle. The altitude is a crucial factor in determining the overall area of the rectangle.
• Describe the role of altitude in the formula for the area of a triangle.
  • The area of a triangle is calculated using the formula $A = \frac{1}{2} \times b \times h$, where $b$ is the base of the triangle and $h$ is the altitude, or perpendicular height, from the base to the opposite vertex. The altitude is a key component of this formula, as it represents the vertical distance between the base and the vertex. By multiplying the base and the altitude and dividing by 2, the formula allows you to calculate the precise area of the triangle based on these two important geometric measurements.
• Analyze how the altitude of a trapezoid is used to determine its area.
  • The formula for the area of a trapezoid is $A = \frac{1}{2} \times (b_1 + b_2) \times h$, where $b_1$ and $b_2$ are the lengths of the parallel bases, and $h$ is the altitude or perpendicular height between the bases. The altitude is a crucial factor in this formula, as it represents the vertical distance between the two parallel sides. By multiplying the average of the base lengths by the altitude and dividing by 2, the formula allows you to calculate the exact area of the trapezoid, taking into account both the base lengths and the height or altitude of the shape.

Related terms

Perpendicular Height: The perpendicular distance from the base of a shape to the opposite side or vertex.

Base:

The line or side of a shape that is considered the bottom or foundation, from which the altitude is measured.

Vertex:

The point where two or more sides of a shape meet, which can be used as a reference point for measuring the altitude.