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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023

Chapter 3

Mathematics in Aviation Maintenance

Example: Find the area of the obtuse triangle shown in

area formula.

Formula: a = 1/2 × (b × h) = 1/2 × (2'6" × 3'2")

Next, convert all dimensions to inches:

Formula: 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:

Formula: a = 1/2 × (30 inches × 38 inches) = 570 square inches

Parallelogram

A parallelogram is a four-sided figure with two pairs of parallel sides. [Figure 3-18] Parallelograms do not necessarily have four right angles.

The formula for the area of a parallelogram is:

Formula: area = length × height = l × h

Trapezoid

A trapezoid is a four-sided figure with one pair of parallel sides. [Figure 3-19] The formula for the area of a trapezoid is:

Formula: area = 1/2 (base1 + base2) × height
Figure 3-13. Formulas to compute area.
Figure 3-13. Formulas to compute area.
Formula: Figure 3-13 formula reference: Rectangle area A = l × w; square area A = s²; triangle area A = ½(b × h) = (b × h) / 2; parallelogram area A = l × h; trapezoid area A = ½(b₁ + b₂) × h; circle area A = πr²; ellipse area A = πab; wing area A = span × mean chord. Source text: Object Area Formula Figure ; Rectangle length × width a = l × w 3-14 ; Square length × width or side × side a = l × w or a = s2 3-15 ; Triangle 1/2 1/2 ( × b × a ( s ( le b e n a × g se t h h × e × i g h h h e e t i ) g i g ÷ h h t ) t 2 ) o o r r a a a = = = 1/2 1/2 (b ( ( × b l × × h ) h h ÷ ) ) o o 2 r r 3 3 - - 1 1 6 7 ; Parallelogram length × height a = l × h 3-18 ; Trapezoid 1/2 (base 1 + base 2 ) × height a = 1/2 (b 1 + b 2 ) × h 3-19 ; Circle π × radius2 a = π × r2 3-20 ; Ellipse π × semi-axis A × semi-axis B a = π × a × b 3-21 ; Wing area span × mean chord a = s × c 3-22
Formula: altitude) is 6 inches? First, substitute the known values in ; the formula. ; a = 1/2 (b1 + b2) × h ; = 1/2 (14 inches + 10 inches) × 6 inches ; a = 1/2 (24 inches) × 6 inches ; = 12 inches × 6 inches = 72 square inches

Circle

A circle is a closed, curved, plane figure. [Figure 3-20] Every point on the circle is an equal distance from the center of the circle. The diameter is the distance across the circle (through the center). The radius is the distance from the center to the edge of the circle. The diameter is always twice the length of the radius. The circumference, or distance around, a circle

Formula: is equal to the diameter times π. ; circumference = c = d π