# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 4

## Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 4

Published $\text {1968}$.

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## $4 \quad$ Geometric Formulas

### Rectangle of Length $b$ and Width $a$

$4.1$: Area of Rectangle
$4.2$: Perimeter of Rectangle

### Parallelogram of Altitude $h$ and Base $b$

$4.3$: Area of Parallelogram
$4.4$: Perimeter of Parallelogram

### Triangle of Altitude $h$ and Base $b$

$4.5$: Area of Triangle in Terms of Side and Altitude
$4.5$: Area of Triangle in Terms of Two Sides and Angle
$4.5$: Heron's Formula
$4.5$: Definition:Semiperimeter
$4.6$: Perimeter of Triangle

### Trapezoid of Altitude $h$ and Parallel Sides $a$ and $b$

$4.7$: Area of Trapezoid
$4.8$: Perimeter of Trapezoid

### Regular Polygon of $n$ Sides each of Length $b$

$4.9$: Area of Regular Polygon
$4.10$: Perimeter of Regular Polygon

### Circle of Radius $r$

$4.11$: Area of Circle
$4.12$: Perimeter of Circle

### Sector of Circle of Radius $r$

$4.13$: Area of Sector
$4.14$: Arc Length of Sector

### Radius of Circle inscribed in a Triangle of Sides $a$, $b$, $c$

$4.15$: Length of Inradius of Triangle

### Radius of Circle circumscribing a Triangle of Sides $a$, $b$, $c$

$4.16$: Length of Circumradius of Triangle

### Regular Polygon of $n$ Sides inscribed in Circle of Radius $r$

$4.17$: Area of Regular Polygon by Circumradius
$4.18$: Perimeter of Regular Polygon by Circumradius

### Regular Polygon of $n$ Sides circumscribing a Circle of Radius $r$

$4.19$: Area of Regular Polygon by Inradius
$4.20$: Perimeter of Regular Polygon by Inradius

### Segment of Circle of Radius $r$

$4.21$: Area of Segment of Circle

### Ellipse of Semi-Major Axis $a$ and Semi-Minor Axis $b$

$4.22$: Area of Ellipse
$4.23$: Perimeter of Ellipse

### Segment of Parabola

$4.24$: Quadrature of Parabola
$4.25$: Arc Length of Parabola

### Rectangular Parallelepiped of Length $a$, Height $l$, Width $c$

$4.26$: Volume of Rectangular Parallelepiped
$4.27$: Surface Area of Rectangular Parallelepiped

### Parallelepiped of Cross-Sectional Area $A$ and Height $h$

$4.28$: Volume of Parallelepiped

### Sphere of Radius $r$

$4.29$: Volume of Sphere
$4.30$: Surface Area of Sphere

### Right Circular Cylinder of Radius $r$ and Height $h$

$4.31$: Volume of Cylinder
$4.32$: Surface Area of Cylinder

### Circular Cylinder of Radius $r$ and Slant Height $l$

$4.33$: Volume of Slanted Cylinder
$4.34$: Surface Area of Slanted Cylinder

### Cylinder of Cross-Sectional Area $A$ and Slant Height $l$

$4.35$: Volume of General Cylinder
$4.36$: Volume of General Cylinder

### Right Circular Cone of Radius $r$ and Height $h$

$4.37$: Volume of Right Circular Cone
$4.38$: Surface Area of Right Circular Cone

### Pyramid of Base Area $A$ and Height $h$

$4.39$: Volume of Pyramid

### Spherical Cap of Radius $r$ and Height $h$

$4.40$: Volume of Spherical Cap
$4.41$: Surface Area of Spherical Cap

### Frustum of Right Circular Cone of Radii $a$, $b$ and Height $h$

$4.42$: Volume of Frustrum
$4.43$: Surface Area of Frustum

### Spherical Triangle of Angles $A$, $B$, $C$ on Sphere of Radius $r$

$4.44$: Area of Spherical Triangle

### Torus of Inner Radius $a$ and Outer Radius $b$

$4.45$: Volume of Torus
$4.46$: Surface Area of Torus

### Ellipsoid of Semi-Axes $a$, $b$, $c$

$4.47$: Volume of Ellipsoid

### Paraboloid of Revolution

$4.48$: Volume of Paraboloid of Revolution

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