Areas of plane geometrical figures



Area  of any plane geometrical figure is a measure of the part of a plane enclosed by it. Let us explore the areas of different polygons, circles, sectors and segments.

Area of any Triangle

Area of a triangle is half the product of its base and the corresponding altitude.

Area of a right triangle

Area of a right triangle is half the product of its perpendicular sides.

Area of an equilateral triangle

Area of an equilateral triangle is a fourth of root three times the square of its side.

Area of a scalene triangle

Area of a scalene triangle can be found with the help of Heron’s formula. It is the square root of the product of its semi perimeter and the difference of all its sides from the semi perimeter.

Area of a quadrilateral

Area of a quadrilateral is half the product of one of its diagonals and the sum of the altitudes form the vertices on either side of the diagonal.

Area of a trapezium

Area of a trapezium is the product of the average of its parallel sides and its altitude

Area of a parallelogram

Area of a parallelogram is the product of its base and altitude.

Area of a rhombus

Area of a rhombus is half the product of its diagonals.

Area of a rectangle

Area of a rectangle is the product of its length and breadth

Area of a square

Area of a square is the square of its side

Area of a square when the diagonal is given

Area of a square is half the square of its diagonal

Area of a regular polygon 

Area of a regular polygon is half the product of its side, apothem and the number of sides.

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides

The areas of a regular pentagon, regular hexagon etc. can be calculated by using this formula.

Area of a circle

Area of a circle is pi times the square of its radius

Area of the  sector of a circle

Area of the sector of a circle is the product of the area of the circle and the ratio of its central angle to 360 degrees.

Area of a segment

Area of a segment is the difference of the area of the sector and the area of the corresponding triangle

Are you ready for a quiz? (take the approximate value of pi as 22/7)

  1. The perimeter of a square is 44 cm. What is its area?
  2. A rectangle and a square have the same perimeter. Which has more area?
  3. The circumference of a circle is 44 cm. What is its area?
  4. The diagonals of a rhombus are 8 cm and 6 cm. Find its area and the length of each side.
  5. A semi circular protractor has a perimeter of 36 cm. What is its area?

Solutions:

  1. 121 sq. cm
  2. square
  3. 154 sq. cm
  4. 24 sq. cm., 5 cm
  5. 77 sq. cm.

Hope you enjoyed the lesson.

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