MENSURATION

1. Area of a General Quadrilateral

1.1. We can find the area of any general quadrilateral by splitting into two triangles.

1.2. Area of a quadrilateral = 1/2 ( diagonal x sum of altitudes drawn on the diagonal from the other two vertices

2. Area of a Polygon

2.1. We can find the area of any polygon by splitting the polygon into triangles, trapeziums, rectangles etc.

3. Surface Area of a Cuboid

3.1. Total surface area = 2 lb + 2 lh + 2bh = 2 ( lb + bh + lh ) cm sq.

4. Right Circular Cylinder

4.1. A right circular cylinder has two circular plane ends. Two plane ends are parallel and are known as bases of the cylinder.

4.2. The line segment joining the centres of two bases is called the axis of the cylinder.

4.3. The radius of the cross-section is called the radius of the cylinder

4.4. The length between the two ends (bases) is called the length or the height of the cylinder

4.5. Axis of cylinder is perpendicular to circular ends. For this reason, this solid figure is known as right circular cylinder. Now onwards, cylinder will always mean a right circular cylinder

4.6. When we rotate a hand fan of rectangular shape very fast, we can clearly see the formation of cylinder

5. Volume of Cube and Cuboid

5.1. Volume of a cuboid = length x breadth x height

5.2. Volume of a cube = side x side x side = (side x side) cube

6. Polyhedrons

6.1. A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex

6.1.1. Prisms are polyhedrons whose base and top are congruent polygons and whose other faces are parallelograms

6.1.2. Pyramids are polyhedrons whose base is a polygon ( of any number of sides ) and whose lateral faces are triangles with a common vertex

6.1.3. Triangular Pyramid is also known as tetrahedron. Tetrahedron is a polyhedron whose all the four faces are triangles

7. Mapping Space around Us

7.1. A map depicts only the location of an object, In relation to other objects.

7.2. Perspective is very important for drawing a picture but it is not relevant for a map.

7.3. Example - A map shows the route that Rahul takes from his home to his school. This is called a route map

8. Introduction

8.1. We will learn to calculate the areas of some plane figures. We will also learn to find the surface area and volume of some solids, such as cuboid, cube and cylinder

9. Area of Trapezium

9.1. We know that trapezium is a quadrilateral, whose one pair of opposite sides are parallel.

9.2. Area of Trapezium = 1/2 x sum of parallel sides x distance between them

10. Surface Area of a Cube

10.1. Total surface area of cube = 6 l sq.

10.2. Lateral surface area of cube = 4 l sq.

11. Surface Area of a Cylinder

11.1. Curved surface area ( lateral surface area ) of a cylinder is 2pierh sq. units, where 'r' is the radius of the cylinder and 'h' is its height.

12. Volume of a Right Circular Cylinder

12.1. Volume of a cylinder (V) = Area of base x height

13. Euler's Formula

13.1. F + V = E + 2

13.2. F + V - E = 2

13.3. This relationship is called Euler's Formula