#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Coordinate Geometry

##### Geometry

##### Coordinate Geometry

##### Mensuration

##### Introduction to Euclid’S Geometry

##### Lines and Angles

- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle

##### Statistics and Probability

##### Triangles

##### Quadrilaterals

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral

##### Areas - Heron’S Formula

##### Surface Areas and Volumes

##### Statistics

##### Algebraic Expressions

##### Algebraic Identities

##### Area

##### Constructions

- Introduction of Constructions
- Basic Constructions
- Some Constructions of Triangles

##### Probability

## Formula

**Cuboid:**A cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. A cuboid looks like a rectangular box. It has 6 faces. Each face has 4 edges. Each face has 4 corners (called vertices).**Surface of a cuboid:**the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying the length by breadth for each of them separately and then adding the six areas together.**Lateral surface area of the cuboid:**Out of the six faces of a cuboid, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cuboid.

## Formula

- Total surface area of cuboid = 2(lb + bh + lh)
- The lateral surface area of a cuboid = 2h(l + b)

## Notes

**Cuboid:**

A cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. A cuboid looks like a rectangular box. It has 6 faces. Each face has 4 edges. Each face has 4 corners (called vertices).

**Total Surface Area of a Cuboid:**

This Figure shows us that the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying the length by breadth for each of them separately and then adding the six areas together.

Let Consider h = height, b = breadth, l = length of cuboid

The total surface area of a cuboid is equal to the sum of all area of 6 rectangles.

Area of □ MNOP = Area of □ QRST = (l × b) cm^{2}

Area of □ MRSN = Area of □ PQTO = (l × h) cm^{2}

Area of □ MPQR = Area of □ NOTS = (b × h) cm^{2}

Total surface area of cuboid = sum of all area of 6 rectangle = 2(l × b) + 2(b × h) + 2(l × h)**Total surface area of cuboid = 2(lb + bh + lh).**

**Lateral Surface area of cuboid:**

Suppose, out of the six faces of a cuboid, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cuboid.

The lateral surface area of a cuboid is 2h(l + b), i.e., 2 × height × sum of length and breadth.

**The lateral surface area of a cuboid = 2h(l + b).**

## Example

How much sheet metal is required to make a closed rectangular box of length 1.5 m, breadth 1.2 m, and height 1.3 m?

length of box = l = 1.5 m,

breadth = b = 1.2 m,

height = h = 1.3 m.

Surface area of box = 2 (l × b + b × h + l × h)

= 2 (1.5 × 1.2 + 1.2 × 1.3 + 1.5 × 1.3)

= 2 (1.80 + 1.56 + 1.95)

= 2 (5.31)

= 10.62 sqm

10.62 sqm of sheet metal will be needed to make the box.

## Example

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## Example

^{2}. What will be the cost of whitewashing if the ceiling of the room is also whitewashed.

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^{2}= Rs. 5

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