This document provides information about plane (2D) and 3D figures in mathematics. It defines common 2D shapes like squares, rectangles, trapezoids, circles, and parallelograms. For each shape, it gives the formula to calculate area, perimeter, and other measurements. It also defines common 3D solids like cubes, cuboids, cylinders, spheres, and cones. For each 3D solid, the summary provides the formula to calculate surface area, volume, and other measurements. The document aims to inform the reader about common geometric shapes and their properties through definitions, examples, and formulas.

1. MATHEMATICS
TOPIC :- MENSURATION
NAME : SAKSHI
B.ED SECONDYEAR

2. LIST OF THE FIGURE
PLANE FIGURE 3D FIGURE
1. SQUARE 1. CUBE
2. RECTANGLE 2. CUBOID
3.TRAPEZIUM 3. CYLINDER
4. CIRCLE 4. SPHERE
5. PARALLELOGRAM 5. CONE

3. PLANE FIGURE (2D FIGURES)
2D FIGURES :- 2D shapes are shapes with two dimensions, such as
width and height. An example of a 2D shape is a
rectangle or a circle. 2D shapes are flat and cannot
be physically held, because they have no depth; a 2D
shape is completely flat.
1. SQUARE
2. RECTANGLE
3. TRAPEZIUM
4. CIRCLE
5. PARALLELOGRAM

4. SQUARE
Square, in geometry, a plane figure with four
equal sides and four right (90°) angles.
Area of the square= a x a
Perimeter of square= 4 x a
a= (side)

5. RECTANGLE
A rectangle is a 2D shape in geometry, having 4 sides and 4
corners. Its two sides meet at right angles. Thus, a rectangle has
4 angles, each measuring 90 ̊
. The opposite sides of a rectangle
have the same lengths and are parallel. Two sides are said to be
parallel, when the distance between them remains the same at all
points.
Area of a rectangle = Length × Width

6. Perimeter of a rectangle = Length + Width + Length + Width
= 2 length + 2Width
= 2 (length + Width)
Diagonal of a Rectangle :-
A rectangle has two diagonals, that bisects each other. Both the diagonals
are equal in length.
D=√L2+W2

7. TRAPEZIUM
A trapezium is a quadrilateral having two parallel sides of unequal length and
the other two sides are non-parallel.The parallel sides of a trapezium are
called bases and the non-parallel sides of a trapezium are called legs. It is also
called a trapezoid.
Area ofTrapezium = 12 x (sum of parallel side) x (Distance between parallel side)
Perimeter of trapezium ABCD = AB + BC + CD +
AD.

9. CIRCLE
A circle is a round shaped figure that has no corners or edges.
In geometry, a circle can be defined as a closed, two-
dimensional curved shape.
Diameter = 2×Radius
Area = πr2
Circumference = 2πr

10. PARALLELOGRAM
A parallelogram is a quadrilateral with two pairs of parallel sides.
The opposite sides of a parallelogram are equal in length, and the
opposite angles are equal in measure. Also, the interior angles on
the same side of the transversal are supplementary. Sum of all the
interior angles equals 360 degrees.
Area = Base × Height
Perimeter = 2 (a+b) units

11. 3D FIGURES
3D FIGURES are solids that consist of 3 dimensions - length, breadth
(width), and height. 3D in the word 3D shapes means three-
dimensional. Every 3D geometric shape occupies some space based on
its dimensions and we can see many 3D shapes all around us in our
day-to-day life. Some examples of 3D shapes are cube, cuboid, cone,
and cylinder.
1. CUBE
2. CUBOID,
3. CYLINDER
4. SPHERE
5. CONE

12. CUBE
a Cube is a solid three-dimensional figure,
which has 6 square faces, 8 vertices and 12
edges. It is also said to be a regular
hexahedron.
Surface Area of Cube = 6a2 in a square units
Volume of cube = a3 cubic units
a
a
Lateral surface area (excluding the top and
bottom faces) = 4 × Area of one face
LSA = 4a2

13. Length of Diagonal of Cube
If a is the length of the side, then,
Length of Diagonal of Face of the Cube = √2 a
Length of Diagonal of Cube = √3 a

14. CUBOID
a cuboid is a solid shape or a three-dimensional shape. A convex
polyhedron that is bounded by six rectangular faces with eight
vertices and twelve edges is called a cuboid. A cuboid is also
called a rectangular prism.
Total Surface Area (TSA) = 2(lb + bh + hl) sq.units
Volume (V) = (l × b × h) cubic units
Diagonal = √(l2 + b2 + h2) units
Perimeter (P) = 4(l + b + h) units
Measure Formula
Lateral Surface Area (LSA) 2h(l + b)
Total Surface Area (TSA) 2(lb + bh + hl)
Volume lbh
Diagonal √(l
2
+ b
2
+ h
2
)
Perimeter 4(l + b + h)

15. CYLINDER
A cylinder is a three-dimensional solid that holds two parallel bases joined by a
curved surface, at a fixed distance. These bases are normally circular in shape
(like a circle) and the center of the two bases are joined by a line segment,
which is called the axis. The perpendicular distance between the bases is the
height, “h” and the distance from the axis to the outer surface is the radius “r”
of the cylinder.
Volume of the Cylinder,V = πr2h cubic units
Total surface area, A = 2πr(r+h) square units
Curved Surface Area = 2πrh square units

16. SPHERE
The sphere is a geometrical figure that is round in
shape. The sphere is defined in a three-dimensional
space. The sphere is three dimensional solid, that has
surface area and volume. Just like a circle, each point
of the sphere is at an equal distance from the center.
MEASURE FORMULA
Diameter of sphere D = 2r, where r is the radius
Surface area of sphere SA = 4πr2 Square units
Volume of sphere V = 4/3 πr3 Cubic Units

17. CONE
A cone is a three-dimensional shape in geometry that narrows smoothly from a
flat base (usually circular base) to a point(which forms an axis to the centre
of base) called the apex or vertex. We can also define the cone as a pyramid
which has a circular cross-section, unlike pyramid which has a triangular cross-
section. These cones are also stated as a circular cone.
Area = πr(l + r)
Volume(V) = ⅓ πr2h cubic units
Slant Height, l = √(r2+h2)
The total surface area of the cone = πrl + πr2

18. Thank You !