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A figure enclosed by three sides is known as a triangle. A triangle has three angles with total sum of 1800 and sum of its any two sides is more than the third side.
It has all three sides equal.
(i) Area =
(ii) Height =
(iii) Perimeter = 3a
Where, a = side, each angle = 600
It has any two sides and two angles equal and altitude bisects the base.
(i) Area =
(ii) Height =
(iii) Perimeter = a + a + b = 2a + b
Where, a= each of two equal sides
b= third side
It has three unequal sides.
Where, and a, b and c are the sides of the triangle.
(iii) Perimeter = a + b + c
Right Angled Triangle
It is a triangle with one angle is equal to 900
(ii) Perimeter = p + b + h
(iii) h2 = p2 + b2 (Pythagoras theorem)
where, p = perpendicular, b = base and h = hypotenuse
Triangle with Height h
This is a triangle with three unequal sides having certain height.
(ii) Perimeter = a + b + c
It is a quadrilateral with opposite sides parallel and equal.
(i) Area = Base × Height = b × h
(ii) Perimeter = 2(a + b)
It is quadrilateral with anyone pair of opposite sides parallel.
Area (Sum of the parallel sides × Height)
Where, a and b are parallel sides and h is the height or perpendicular distance between a and b.
It is a parallelogram with all 4 sides equal. The opposite angle in a rhombus are equal but they are not right angle.
(iii) Perimeter = 4a
Where, a = side, d1 and d2 are diagonals.
- It is a parallelogram with equal opposite sides and each angle is equal to 900.
(i) Area = Length × Breadth = l × b
(ii) Perimeter = 2(l + b)
(iv) Area of 4 walls of rectangular room
= 2 × (l + b × h)
Where, l = length, b = breadth, h = height
It is a parallelogram with all 4 sides equal and each angle is equal to 900.
(ii) Perimeter = 4 × side = 4a
Where, a = side, d = diagonal
- In regular polygons, all sides and all interior angles are equal. A polygon is called pentagon, hexagon, heptagon, octagon, nanogon and decagon according as it contains 5, 6, 7, 8, 9 and 10 sides respectively.
If each side of a regular polygon of n sides = a
(i) Area of regular pentagon
(ii) Area of regular hexagon
(iii) Area of regular octagon
(iv) Each exterior angle
(v) Each interior angle = 1800 – Exterior angle
(vi) Number of diagonals
It is a plane figure enclosed by a line on which every point is equally distant form a fixed point (centre) inside the curve.
(i) Area = πr2
(ii) Circumference (perimeter) = 2πr
(iii) Diameter = 2r
(iv) Length of the arc
(v) Area of sector
where, r = radius
Incase of circular ring,
(ii) Difference in circumference of both the rings
where, R = radius of bigger ring
and r = radius of smaller ring