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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023

Chapter 3

Mathematics in Aviation Maintenance

Computing Area of Two-Dimensional Solids

Area is a measurement of the amount of surface of an object. Area is usually expressed in such units as square inches or square centimeters for small surfaces or in square feet or square meters for larger surfaces.

Figure 3-13 summarizes the formulas for computing the area of two-dimensional solids.

Rectangle

A rectangle is a four-sided figure with opposite sides of equal length and parallel to each other. [Figure 3-14] All of the angles are right angles. A right angle is a 90° angle. The rectangle is a very familiar shape in mechanics. The formula for the area of a rectangle is:

Formula: area = length × width = l × w

Example: An aircraft floor panel is in the form of a rectangle having a length of 24 inches and a width of 12 inches. What is the area of the panel expressed in square inches? First, determine the known values and substitute them in the formula.

Formula: a = l × w = 24 inches × 12 inches = 288 square inches

Square

A square is a four-sided figure with all sides of equal length and opposite sides are parallel to each other. [Figure 3-15] All angles are right angles. A right angle is a 90° angle. The formula for the area of a square is:

Formula: area = length × width = l × w

Since the length and the width of a square are the same value, the formula for the area of a square can also be written as:

Formula: area = side × side = s2

Example: What is the area of a square access plate whose side measures 25 inches? First, determine the known value and substitute it in the formula.

Formula: a = l × w = 25 inches × 25 inches = 625 square inches

Triangle

A triangle is a three-sided figure. The sum of the three angles in a triangle is always equal to 180°. Triangles are often classified by their sides. An equilateral triangle has 3 sides of equal length. An isosceles triangle has 2 sides of equal length. A scalene triangle has three sides of differing lengths.

Triangles can also be classified by their angles. An acute triangle has all three angles less than 90°. A right triangle has one right angle (a 90° angle). An obtuse triangle has one angle greater than 90°. Each of these types of triangles is shown in Figure 3-16.

The formula for the area of a triangle is

Formula: area = 1/2 × (base × height) = 1/2 × (b × h)