Formulas for Perimeter, Area and Volume

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m1422

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formulas-perimeter-area-volume

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Geometry

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Secondary I

Secondary II

Secondary III

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Mathematics

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Contenu

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Anchor

Title

Summary Table of Formulas for the Perimeter and Area of Plane Figures

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summary-plane-figures

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Anchor

Title

Summary Table of the Area and Volume Formulas for Solids

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summary-solids

Title (level 2)

Summary Table of Formulas for the Perimeter and Area of Plane Figures

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summary-plane-figures

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Corps

Perimeter, generally denoted |P,| is the measure of the contour of a figure. To calculate the perimeter, we add the measures of all the sides. In the case of the circle, the perimeter is called circumference and is denoted |C.|
Area, generally denoted |A,| is the surface occupied by an object (in a 2 dimensional plane). Area is calculated in squared units (u²).

Corps

Plane Figure	Perimeter	Area
Triangle	\|\|P=\color{#3A9A38}{a}+\color{#3B87CD}{b}+\color{#FF55C3}{c}\|\|	\|\|A=\dfrac{\color{#3B87CD}{b}\times\color{#EC0000}{h}}{2}\|\|
Square	\|\| $\begin{align} P&=\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}\\ &=4\color{#3A9A38}{s} \end{align}$ \|\|	\|\| $\begin{align} A&=\color{#3A9A38}{s}\times\color{#3A9A38}{s}\\ &=\color{#3A9A38}{s}^2 \end{align}$ \|\|
Rectangle	\|\| $\begin{align} P&=\color{#3B87CD}{b}+\color{#3B87CD}{b}+\color{#EC0000}{h}+\color{#EC0000}{h}\\ &=2\color{#3B87CD}{b}+2\color{#EC0000}{h}\\ &=2(\color{#3B87CD}{b}+\color{#EC0000}{h}) \end{align}$ \|\|	\|\|A=\color{#3B87CD}{b}\times\color{#EC0000}{h}\|\|
Parallelogram	\|\| $\begin{align} P&=\color{#FF55C3}{a}+\color{#FF55C3}{a}+\color{#3B87CD}{b}+\color{#3B87CD}{b}\\ &=2\color{#FF55C3}{a}+2\color{#3B87CD}{b}\\ &=2(\color{#FF55C3}{a}+\color{#3B87CD}{b}) \end{align}$ \|\|	\|\|A=\color{#3B87CD}{b}\times\color{#EC0000}{h}\|\|
Rhombus	\|\| $\begin{align} P&=\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}\\ &=4\color{#3A9A38}{s} \end{align}$ \|\|	\|\|A=\dfrac{\color{#FF55C3}{D}\times\color{#3B87CD}{d}}{2}\|\|
Trapezoid	\|\|P=\color{#3B87CD}{b}+\color{#3A9A38}{a}+\color{#FA7921}{B}+\color{#FF55C3}{c}\|\|	\|\|A=\dfrac{(\color{#3B87CD}{b}+\color{#FA7921}{B})\times\color{#EC0000}{h}}{2}\|\|
Regular Polygon	\|\|P=n\times\color{#3A9A38}{s}\|\|	\|\|A=\dfrac{\color{#3A9A38}{s}\color{#FA7921}{a}n}{2}\|\|
Circle	\|\|C=2\pi\color{#3A9A38}{r}\|\|	\|\|A=\pi\color{#3A9A38}{r}^2\|\|

Title (level 2)

Summary Table of the Area and Volume Formulas for Solids

Title slug (identifier)

summary-solids

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Content

Corps

The area of the base, generally denoted |A_b,| is the surface occupied by the figure(s) that serve as base for the solids in question.
The lateral area, generally denoted |A_L,| is the surface occupied by the figures which do not serve as bases for the solids in question.
The total area, generally denoted |A_T,| is the total surface covered by all the figures forming the solids in question.
The volume, generally denoted |V,| is the portion of space occupied by a solid (in a 3 dimensional space). The volume is calculated in cubic units (u³).

Corps

Solid	Area Formula	Volume Formula
Cube	Area of a Cube\|\| $\begin{align} A_b&=\color{#3a9a38}{s}^2\\\\ A_L&=4\color{#3a9a38}{s}^2\\\\ A_T&=6\color{#3a9a38}{s}^2 \end{align}$ \|\|	Volume of a Cube\|\|V=\color{#3a9a38}{s}^3\|\|
Prism	Area of Prisms\|\| $\begin{align} \color{#3b87cd}{A_b}&=\text{formula associated with the figure}\\\\ A_L&=P_b\times\color{#ec0000}{h}\\\\ A_T&=A_L+2\color{#3b87cd}{A_b} \end{align}$ \|\|	Volume of Prisms\|\|V=\color{#3b87cd}{A_b}\times\color{#ec0000}{h}\|\|
Pyramid	Area of Pyramids\|\| $\begin{align} \color{#3b87cd}{A_b}&=\text{formula associated with the figure}\\\\ A_L&=\dfrac{P_b\times\color{#fa7921}{a}}{2}\\\\ A_T&=A_L+\color{#3b87cd}{A_b} \end{align}$ \|\|	Volume of Pyramids\|\|V=\dfrac{\color{#3b87cd}{A_b}\times\color{#ec0000}{h}}{3}\|\|
Sphere	Area of a Sphere\|\|A_T=4\pi\color{#3a9a38}{r}^2\|\|	Volume of a Sphere\|\|V=\dfrac{4\pi\color{#3a9a38}{r}^3}{3}\|\|
Cylinder	Area of Cylinders\|\| $\begin{align} \color{#3b87cd}{A_b}&=\pi\color{#3a9a38}{r}^2\\\\ A_L&=2\pi\color{#3a9a38}{r}\color{#ec0000}{h}\\\\ A_T&=A_L+2\color{#3b87cd}{A_b} \end{align}$ \|\|	Volume of Cylinders\|\|V=\color{#3b87cd}{A_b}\times\color{#ec0000}h\|\|
Cone	Area of Cones \| $\begin{align}\color{#3b87cd}{A_b}&=\pi\color{#3a9a38}r^2\\\\ A_L&=\pi\color{#3a9a38}r\color{#fa7921}a\\\\ A_T&=A_L+\color{#3b87cd}{A_b}\end{align}$ \|	Volume of Cones\|\|V=\dfrac{\color{#3b87cd}{A_b}\times\color{#ec0000}h}{3}\|\|

Title (level 2)

Plane Figure	Perimeter	Area
Triangle	\|\|P=\color{#3A9A38}{a}+\color{#3B87CD}{b}+\color{#FF55C3}{c}\|\|	\|\|A=\dfrac{\color{#3B87CD}{b}\times\color{#EC0000}{h}}{2}\|\|
Square	\|\| $\begin{align} P&=\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}\\ &=4\color{#3A9A38}{s} \end{align}$ \|\|	\|\| $\begin{align} A&=\color{#3A9A38}{s}\times\color{#3A9A38}{s}\\ &=\color{#3A9A38}{s}^2 \end{align}$ \|\|
Rectangle	\|\| $\begin{align} P&=\color{#3B87CD}{b}+\color{#3B87CD}{b}+\color{#EC0000}{h}+\color{#EC0000}{h}\\ &=2\color{#3B87CD}{b}+2\color{#EC0000}{h}\\ &=2(\color{#3B87CD}{b}+\color{#EC0000}{h}) \end{align}$ \|\|	\|\|A=\color{#3B87CD}{b}\times\color{#EC0000}{h}\|\|
Parallelogram	\|\| $\begin{align} P&=\color{#FF55C3}{a}+\color{#FF55C3}{a}+\color{#3B87CD}{b}+\color{#3B87CD}{b}\\ &=2\color{#FF55C3}{a}+2\color{#3B87CD}{b}\\ &=2(\color{#FF55C3}{a}+\color{#3B87CD}{b}) \end{align}$ \|\|	\|\|A=\color{#3B87CD}{b}\times\color{#EC0000}{h}\|\|
Rhombus	\|\| $\begin{align} P&=\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}+\color{#3A9A38}{s}\\ &=4\color{#3A9A38}{s} \end{align}$ \|\|	\|\|A=\dfrac{\color{#FF55C3}{D}\times\color{#3B87CD}{d}}{2}\|\|
Trapezoid	\|\|P=\color{#3B87CD}{b}+\color{#3A9A38}{a}+\color{#FA7921}{B}+\color{#FF55C3}{c}\|\|	\|\|A=\dfrac{(\color{#3B87CD}{b}+\color{#FA7921}{B})\times\color{#EC0000}{h}}{2}\|\|
Regular Polygon	\|\|P=n\times\color{#3A9A38}{s}\|\|	\|\|A=\dfrac{\color{#3A9A38}{s}\color{#FA7921}{a}n}{2}\|\|
Circle	\|\|C=2\pi\color{#3A9A38}{r}\|\|	\|\|A=\pi\color{#3A9A38}{r}^2\|\|

Solid	Area Formula	Volume Formula
Cube	Area of a Cube\|\| $\begin{align} A_b&=\color{#3a9a38}{s}^2\\\\ A_L&=4\color{#3a9a38}{s}^2\\\\ A_T&=6\color{#3a9a38}{s}^2 \end{align}$ \|\|	Volume of a Cube\|\|V=\color{#3a9a38}{s}^3\|\|
Prism	Area of Prisms\|\| $\begin{align} \color{#3b87cd}{A_b}&=\text{formula associated with the figure}\\\\ A_L&=P_b\times\color{#ec0000}{h}\\\\ A_T&=A_L+2\color{#3b87cd}{A_b} \end{align}$ \|\|	Volume of Prisms\|\|V=\color{#3b87cd}{A_b}\times\color{#ec0000}{h}\|\|
Pyramid	Area of Pyramids\|\| $\begin{align} \color{#3b87cd}{A_b}&=\text{formula associated with the figure}\\\\ A_L&=\dfrac{P_b\times\color{#fa7921}{a}}{2}\\\\ A_T&=A_L+\color{#3b87cd}{A_b} \end{align}$ \|\|	Volume of Pyramids\|\|V=\dfrac{\color{#3b87cd}{A_b}\times\color{#ec0000}{h}}{3}\|\|
Sphere	Area of a Sphere\|\|A_T=4\pi\color{#3a9a38}{r}^2\|\|	Volume of a Sphere\|\|V=\dfrac{4\pi\color{#3a9a38}{r}^3}{3}\|\|
Cylinder	Area of Cylinders\|\| $\begin{align} \color{#3b87cd}{A_b}&=\pi\color{#3a9a38}{r}^2\\\\ A_L&=2\pi\color{#3a9a38}{r}\color{#ec0000}{h}\\\\ A_T&=A_L+2\color{#3b87cd}{A_b} \end{align}$ \|\|	Volume of Cylinders\|\|V=\color{#3b87cd}{A_b}\times\color{#ec0000}h\|\|
Cone	Area of Cones \| $\begin{align}\color{#3b87cd}{A_b}&=\pi\color{#3a9a38}r^2\\\\ A_L&=\pi\color{#3a9a38}r\color{#fa7921}a\\\\ A_T&=A_L+\color{#3b87cd}{A_b}\end{align}$ \|	Volume of Cones\|\|V=\dfrac{\color{#3b87cd}{A_b}\times\color{#ec0000}h}{3}\|\|