Mensuration and Measurement Formulae - Perimeter and Area of Basic Shapes

Nov 4, 2026

Uploaded by miraaa_2004

Mensuration and measurement formulas covering perimeter, area, surface area, and volume for common 2D and 3D shapes. It provides perimeter relations for triangles, rectangles, squares, quadrilaterals, parallelograms, and circles, including circle circumference forms using radius and diameter. It also lists area formulas for rectangles, squares, triangles, and circles. For solids, it includes surface-area expressions for rectangular prisms, cuboids, cones, and cylinders, plus volume formulas for rectangular prisms, cubes, and cylinders.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Perimeter formulas

Triangle, rectangle, square, quadrilateral, parallelogram

Circle perimeter (circumference)

Area formulas

Rectangle, square, triangle, circle

Surface area and volume formulas

Rectangular prism and cuboid

Cone and cylinder

Volumes of prism, cube, and cylinder

| Mensuration and Measurement Formulae The perimeter of a triangle:
If the three sides of a triangle are represented by the letters a, b, and c, then the perimeter of the triangle = a + b + c, and you must take care to ensure that all the three sides of the triangle are in the same units.

The perimeter of a rectangle:
Perimeter of rectangle = a + b + a + b = 2a + 2b = 2(a + b) | | --- | | | | | | The perimeter of a square:
Perimeter of square = a + a + a + a = 4a | | --- | | | | The perimeter of a quadrilateral:
A quadrilateral is just a closed space with all sides of different lengths, and all internal angles have different values. That is why when you need to calculate the perimeter of a quadrilateral you add up the value of the four sides. There is no easy formula to use.
| The perimeter of a parallelogram: Perimeter of parallelogram = a + b + a + b = 2a + 2b = 2 (a + b) The perimeter of a circle: Perimeter = 2 x π x r = 2 πr OR Perimeter = π D, Where, r is the radius of the circle and D is the diameter. The perimeter of a circle is also referred to as its circumference. You can check out this widget to see the interplay of different combinations of radius and circumference. Area of a rectangle Area of rectangle = length x breadth = l x b Area of a square: Area of square = a x a = a2 Area of a triangle Area of triangle = ½ x b x h Area of a Circle: Area of a circle = πr2 OR Area of a circle = πD2/4 , Where r is the radius of the circle and D is the diameter. Surface Area of Rectangular Prism: Surface area of rectangular prisms = sum of surface area of six faces = lb + lb + bh + bh + lh + lh = 2 (lb + bh + lh) Surface Area of a Cuboid Surface Area of cuboid = 2 (lb + bh + lh) = 2(a2 + a2 + a2 ) = 6a2 Surface Area of a Cone: Surface Area of Cone = area of curved surface + area of circle = πr + πr2 = πr (l + r) Surface Area of a Cylinder: Surface Area of cylinder = area of circle at top/front + area of circle at bottom/back + area of curved surface = πr2 + πr2 + 2πrh = πr (r + r + 2h) = πr (2r + 2h) = 2πr (r + h) Volume of a rectangular prism: Let us represent the length as ‘l’, breadth as ‘b’and height as ‘h’. Then, the Volume of prism = l x b x h = lbh Volume of cube: Volume of cube = a x a x a = a3 Volume of cylinder: Volume of cylinder = π x r x r x h = πr2 h. Try this widget to check if you have understood the formula for calculating the volume of a cylinder properly.

FAQs

What is the general perimeter formula for a triangle and what must be checked?

If the triangle’s sides are a, b, and c, then the perimeter is a + b + c. Ensure all three sides are measured in the same units.

What are the area formulas for a rectangle and a square?

Rectangle area is length × breadth (l × b). Square area is a × a, written as a².

How do you calculate surface area and volume for a cylinder?

Surface area is 2πr(r + h). Volume is πr²h, using r as the radius and h as the height.

Nov 4, 2026

Uploaded by miraaa_2004