Mensuration — Triangle, Quadrilaterals, Regular Polygons and Circle
What is Mensuration — Triangle, Quadrilaterals, Regular Polygons and Circle?
The branch of mathematics concerned with the measurement of geometric figures, such as length, area, and volume.
Key formula / rule: Area of Triangle (Base & Height)
Key points
- To be able to calculate the area and perimeter of triangles, quadrilaterals, regular polygons, and circles.
- To understand and apply different formulas based on the given information.
- To solve problems involving composite shapes made from these basic figures.
- To relate different geometric properties and solve problems using them.
Common exam trap
Confusing area and perimeter formulas.
Definitions
- Term
Mensuration
- Meaning
The branch of mathematics concerned with the measurement of geometric figures, such as length, area, and volume.
- Term
Perimeter
- Meaning
The continuous line forming the boundary of a closed geometric figure; the total length of the boundary.
- Term
Area
- Meaning
The extent or measurement of a surface or piece of land.
- Term
Equilateral Triangle
- Meaning
A triangle in which all three sides are equal and all three angles are equal (60 degrees).
- Term
Isosceles Triangle
- Meaning
A triangle with at least two sides of equal length and two angles of equal measure.
- Term
Scalene Triangle
- Meaning
A triangle that has three unequal sides and three unequal angles.
- Term
Right-angled Triangle
- Meaning
A triangle in which one angle is a right angle (90 degrees).
- Term
Regular Polygon
- Meaning
A polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
- Term
Apothem
- Meaning
A line segment from the center of a regular polygon to the midpoint of a side.
- Term
Chord
- Meaning
A line segment connecting two points on a circle's circumference.
- Term
Tangent
- Meaning
A line that touches a circle at exactly one point.
- Term
Sector
- Meaning
A portion of a circle enclosed by two radii and an arc.
Learning objectives
To be able to calculate the area and perimeter of triangles, quadrilaterals, regular polygons, and circles.
To understand and apply different formulas based on the given information.
To solve problems involving composite shapes made from these basic figures.
To relate different geometric properties and solve problems using them.
Formulae
- Name
Area of Triangle (Base & Height)
- Note
Standard formula for any triangle.
- Expression
1/2 * base * height
- Name
Heron's Formula (Triangle)
- Note
Used when all three sides are known.
- Expression
s = (a+b+c)/2, Area = sqrt(s(s-a)(s-b)(s-c))
- Name
Area of Equilateral Triangle
- Note
Specific formula for equilateral triangles.
- Expression
(√(3)/4) * side2
- Name
Area of Square
- Note
Side length squared.
- Expression
side2
- Name
Perimeter of Square
- Note
Sum of all four equal sides.
- Expression
4 * side
- Name
Area of Rectangle
- Note
Product of length and width.
- Expression
length * width
- Name
Perimeter of Rectangle
- Note
Twice the sum of length and width.
- Expression
2 * (length + width)
- Name
Area of Parallelogram
- Note
Product of base and perpendicular height.
- Expression
base * height
- Name
Area of Rhombus
- Note
Half the product of the diagonals.
- Expression
1/2 * diagonal1 * diagonal2
- Name
Area of Trapezium
- Note
Half the product of the sum of parallel sides and the perpendicular height.
- Expression
1/2 * (sum of parallel sides) * height
- Name
Area of Circle
- Note
Π × the square of the radius.
- Expression
π * r2
- Name
Circumference of Circle
- Note
Twice the product of π and the radius.
- Expression
2 * π * r
- Name
Area of Regular Polygon
- Note
n = number of sides, s = side length. Alternatively, (1/2) * Perimeter * Apothem.
- Expression
(n * s2) / (4 * tan(180/n))
- Name
Sum of Interior Angles (Polygon)
- Note
n = number of sides.
- Expression
(n-2) * 180 degrees
- Name
Each Interior Angle (Regular Polygon)
- Note
n = number of sides.
- Expression
(n-2) * 180 / n degrees
Prerequisites
Basic arithmetic operations.
Understanding of basic algebraic expressions and equations.
Knowledge of basic geometry terms (lines, angles, vertices).
Common mistakes
Confusing area and perimeter formulas.
Incorrectly applying formulas for specific types of triangles or quadrilaterals.
Errors in calculating the apothem or radius for regular polygons.
Using approximate values for π without considering the required precision.
Misinterpreting diagrams or given information.
Keywords
Mensuration
Area
Perimeter
Triangle
Quadrilateral
Polygon
Circle
Geometry
Formulas
SSC CGL
Practice preview
Find the area of a triangle with base 10 cm and height 8 cm.…
easy
A sector of a circle has a radius of 14 cm and an angle of 90 degrees. What is its area? (Use pi = 22/7)…
medium
If the side of a square is 6 cm, what is its area?…
easy