Computing Area of Two-dimensional Solids – Triangles

in Aviation Mathematics

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 length. 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 1-15.

Figure 1-15. Types of triangles.

Figure 1-15. Types of triangles.

The formula for the area of a triangle is

Area = 1⁄2 × (Base × Height) = 1⁄2 × (B × H)

Example: Find the area of the obtuse triangle shown in Figure 1-16. First, substitute the known values in the area formula.

Figure 1-16. Obtuse triangle.

Figure 1-16. Obtuse triangle.

A = 1⁄2 × (B × H) = 1⁄2 × (2’6″ × 3’2″)

Next, convert all dimensions to inches:

2’6″ = (2 × 12″) + 6″ = (24 + 6) = 30 inches

3’2″ = (3 × 12″) + 2″ = (36 + 2) = 38 inches

Now, solve the formula for the unknown value:

A = 1⁄2 × (30 inches × 38 inches) = 570 square inches

 

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