Home Mathematics MATHEMATICS: A Textbook for Grade 11   Chapter 6: Mensuration

E-Lecture - Important Points
  • The distance from the center of a circle to any point on its boundary is called radius of circle.
  • A line segment passing through the center that connects two points on the boundary is called diameter of a circle.
  • Any line segment touching the circle at two different points on its boundary is called chord of a circle.
  • The set of points on a circle (any part of a circle) contained in one of the two half-planes determined by the line through any two distinct points of a circle are called an arc of a circle.
  • The perpendicular from the center of a circle to a chord bisects the chord. In other words, the perpendicular bisector of a chord passes through the center of the circle.
  • Equal chords of a circle are equidistant from the center.
  • When two circles intersect each other, then the line joining their centers bisects their common chord at right angles.
  • Products of intercepts of two intersecting chords are equal.
  • A central angle of a circle is an angle whose vertex is the center of the circle and whose sides are radii of the circle.
  • The angle subtended by an arc at the center of a circle is double the size of the angle subtended by the same arc at the circle.
  • An inscribed angle is an angle whose vertex lies on the circle and whose sides are chords of the circle.
  • The measure of an inscribed angle is equal to half the measure of its intercepted arc.
  • If two inscribed angles intercept the same arc, then these angles are congruent.
  • The measure of an angle formed by two chords intersecting inside a circle is half the sum of the measure of the arcs subtending the angle and its vertical opposite angle.
  • If a line intersects a circle at exactly one point, then the line is called a tangent line of the circle.
  • The point at which the tangent intersects the circle is called the point of tangency. (or point of contact)
  • If a line intersects a circle at two points, then the line is called a secant line of the circle.
  • Tangent to the circle is perpendicular to the radius of the circle at the point of contact.
  • If two tangents are drawn from an external point of the circle, then they are of equal lengths.
  • If from a point outside a circle, a secant and a tangent are drawn, then the tangent is the mean proportional between the secant and its external segment.
  • For any circle, the angle between a tangent and a chord through the point of contact of the tangent is equal to the angle made by the chord in the alternate segment.
  • The perimeter of a triangle with length of sides a, b and c units is given by the formula: P = a + b + c
  • The perimeter (P) of a rectangle whose length is ℓ and width is ω is given by the formula: P = 2 × (ℓ + ω)
  • The perimeter of a square whose side length is s is given by the formula: P = 4s
  • The perimeter of a parallelogram with adjacent sides a and b is given by the formula: P = 2 × (a + b)
  • The perimeter of a rhombus whose side length is s is given by the formula: P = 4s
  • If the length of the four sides of a trapezium are a, b, c and d units, then, the perimeter of the trapezium is given by the formula: P = a + b + c + d
  • Area occupied by a rectangle within its boundary is called the area of the rectangle.
  • The area (A) of rectangle is the product of its length (ℓ) and width (ω). That is, A = ℓ × ω
  • Suppose a and b are the lengths of parallel sides of a parallelogram and h is the corresponding height of the parallelogram, then based on the length of sides and height of it, the formula for its area is given by: A = b × h
  • The area A of a rhombus with a base of length b and with corresponding height of h is given by: A = b × h
  • Area A of a triangle whose base has length b and whose corresponding height has length h is given by
  • The circumference, C of a circle with radius r or diameter d is given by the formula: C= πd or C = 2πr.
  • The area A of a circle whose radius has length r is given by the formula: A = πr2.
  • The perimeter, P and area, A of a sector, whose central angle is θ and radius r is given by: P = 2r + ℓ. where ℓ is arc length.
PREV
Go Back to Chapter Details
Browse Chapter