Content code
m1422
Slug (identifier)
formulas-perimeter-area-volume
Parent content
Geometry
Grades
Secondary I
Secondary II
Secondary III
Topic
Mathematics
Content
Contenu
Links
Type
Anchor
Title
Summary Table of Formulas for the Perimeter and Area of Plane Figures
Anchor
summary-plane-figures
Type
Anchor
Title
Summary Table of the Area and Volume Formulas for Solids
Anchor
summary-solids
Title (level 2)
Summary Table of Formulas for the Perimeter and Area of Plane Figures
Title slug (identifier)
summary-plane-figures
Contenu
Content
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

Triangle with 3 sides and a height identified

||P=\color{#3A9A38}{a}+\color{#3B87CD}{b}+\color{#FF55C3}{c}||

||A=\dfrac{\color{#3B87CD}{b}\times\color{#EC0000}{h}}{2}||

Square

Square with 4 sides identified

||\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

Rectangle with 2 bases and 2 heights identified

||\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

Parallelogram with 2 pairs of sides and a height identified

||\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

Rhombus with 2 diagonals and 4 sides identified

||\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

Trapezoid with 2 bases, 2 sides and a height identified

||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

Regular polygon with n sides and an apothem identified

||P=n\times\color{#3A9A38}{c}||

||A=\dfrac{\color{#3A9A38}{s}\color{#FA7921}{a}n}{2}||

Circle

Circle with a radius identified

||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
Contenu
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

Cube with a side identified

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

Prism with a height identified

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

Pyramid with a height and an apothem identified

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

Sphere with a radius identified

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

Cylinder with a height and radius identified

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

Cone with a height and radius identified

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)
See Also
Title slug (identifier)
see-also
Contenu
Links
Type
Internal
Title
The Perimeter and Area of Plane Figures
Internal link
/en/students/vl/mathematics/perimeter-and-area-of-plane-figures-m1478
Type
Internal
Title
The Perimeter and Area of Quadrilaterals
Internal link
/en/students/vl/mathematics/perimeter-and-area-of-quadrilaterals-m1199
Type
Internal
Title
Surface Area and Volume of Solids
Internal link
/en/students/vl/mathematics/area-volume-solids-m1243