Explain the properties of rectangle, square, triangle and circle with the he formulae of its peri meter and area
Answers
Answer:
Perimeter:
The length of the boundary of a closed figure is called the perimeter of the plane figure. The units of perimeter are same as that of length, i.e., m, cm, mm, etc.
Area:
A part of the plane enclosed by a simple closed figure is called a plane region and the measurement of plane region enclosed is called its area.
Area is measured in square units.
Perimeter and Area of Rectangle:
● The perimeter of rectangle = 2(l + b).
● Area of rectangle = l × b; (l and b are the length and breadth of rectangle)
● Diagonal of rectangle = √(l² + b²)
Perimeter and Area of the Square:
● Perimeter of square = 4 × S.
● Area of square = S × S.
● Diagonal of square = S√2; (S is the side of square)
Perimeter and Area of the Triangle:
● Perimeter of triangle = (a + b + c); (a, b, c are 3 sides of a triangle)
● Area of triangle = √(s(s - a) (s - b) (s - c)); (s is the semi-perimeter of triangle)
● S = 1/2 (a + b + c)
● Area of triangle = 1/2 × b × h; (b base , h height)
● Area of an equilateral triangle = (a²√3)/4; (a is the side of triangle)
Perimeter and Area of the Parallelogram:
● Perimeter of parallelogram = 2 (sum of adjacent sides)
● Area of parallelogram = base × height
Perimeter and Area of the Rhombus:
● Area of rhombus = base × height
● Area of rhombus = 1/2 × length of one diagonal × length of other diagonal
● Perimeter of rhombus = 4 × side
Perimeter and Area of the Trapezium:
● Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)
= 1/2 (p₁ + p₂) × h (p₁, p₂ are 2 parallel sides)
Circumference and Area of Circle:
● Circumference of circle = 2πr
= πd
Where, π = 3.14 or π = 22/7
r is the radius of circle
d is the diameter of circle
● Area of circle = πr²
● Area of ring = Area of outer circle - Area of inner circle.
Properties of Square :
Opposite sides are parallel, with all sides being equal.
A square has four lines of symmetry.
The order of rotational symmetry is 4.
The diagonals bisect each other at 90° or right angles.
All sides are equal.
Opposite sides are equal and parallel.
All angles are equal to 90 degrees.
TRIANGLE
The properties of the triangle are: The sum of all the angles of a triangle(of all types) is equal to 1800. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
CIRCLE:
Circles having equal radii are congruent.
Circles having different radii are similar.
The central angle which intercepts an arc is the double of any inscribed angle that intercepts the same arc (proof).
The radius perpendicular to a chord bisects the chord.
The chords equidistant from the center are equal in length.
Properties of a rectangle:
It has 2 pairs of equal sides that are opposite to each other.
The four interior and exterior angles are 90 deg.
The two diagonals are equal.
A circle can circumscribe a rectangle but a rectangle cannot circumscribe a circle.
Product of two adjacent sides gives the area.