3.1 MENSURATION

Plane areas, surface areas, and volumes of the regular geometric shapes and solids illustrated herein can be calculated by using the formulas which appear next to the respective figure numbers in parentheses.

Figure 3.1: Triangle.

Figure 3.2: Triangle.

Figure 3.3: Rectangle.

where A = area

• V = volume

• R = radius

• S = surface area

• r = radius

• C = circumference

• n = number of sides

• L = length of a side

Figure 3.4: Parallelogram.

Figure 3.5: Rhombus.

Figure 3.6: ( a) Trapezoid: ( b) trapezium.

Figure 3.7: Regular polygon.

The radius of a circle inscribed in any triangle whose sides are a, b, and c is

where s = (1/2) ( a + b + c). The radius of the circumscribed circle is

Area of an inscribed polygon is

where r = radius of the circumscribed circle and n = number of sides.

Figure 3.8: Inscribed circle.

Figure 3.9: Circumscribed circle.

Figure 3.10: Inscribed polygon.

Figure 3.11: Circumscribed polygon.

Figure 3.12: Circle.

where r = radius of the inscribed circle and n = number of sides. Circumference of a circle:

Area of a circle:

Length of arc L:

where ? is in radians and L = r ?. Length of chord AB:

Figure 3.13: Area.

Figure 3.14: Arc.

Figure 3.15: Chord.

The area of the sector:

where L is the length of...