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Chapter 3: C. Basic Geometry 23
Table 3.2 Calculation of perimeter and circumference of basic geometric shapes. Continued
Shape Example Formula
Circle
D
r
Circumference = 2p r = p D
where r is radius and
D is diameter.
Part I.C
A parallelogram has two sides equal to 26 mm and a top and
base each equal to 40 mm. Its perimeter is (2 × 26 mm) + (2 × 40 mm)
= 132 mm.
A trapezoid has sides of length 12, 15, 24, and 27 cm. Its perimeter is
then (12 cm + 15 cm + 24 cm + 27 cm) = 78 cm.
A regular hexagon (meaning one with all sides the same length) has
sides of length 8.0 cm. Its perimeter is then 6 × 8.0 cm = 48.0 cm.
A right triangle (meaning that the triangle has a 90-degree angle) has
a base of 65 mm, a height of 120 mm, and a hypotenuse of 136.47 mm.
Its perimeter is (65 mm + 120 mm + 136.47 mm) = 321.47 mm.
A triangle has sides with lengths 20 cm, 34 cm, and 40 cm. Its perimeter
is (20 cm + 34 cm + 40 cm) = 94 cm.
A circle has a radius of 25 inches, hence a diameter of 50 inches. Its
circumference is (2 × p × 25 in) = (p × 50 in) = 157.08 in. Note: since
the formula involves pi, when at all possible use a calculator to find
circumference to avoid round-off errors.
VOLUME OF BASIC GEOMETRIC SHAPES
Volume (V) is expressed in terms of cubic units, such as cm 3 or ft 3 . Formulas for
calculating volume are shown in Table 3.3.
Examples of Volume Calculations
A square prism has length, width, and height equal to 23 cm, 12 cm, and
30 cm, respectively. Its volume is (23 cm × 12 cm × 30 cm) = 8280 cm 3 .
A cube has sides of length 13 inches. Its volume is then (13 in) 3 = (13 in ×
13 in × 13 in) = 2197 in 3 .