# Grade VIII. Mathematics Geometry Notes. #GrowWithGreen

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1 Grade VIII Mathematics Geometry Notes #GrowWithGreen

2 Polygons can be classified according to their number of sides (or vertices). The sum of all the interior angles of an n -sided polygon is given by, ( n 2) 180. The sum of measures of all exterior angles of a polygon is 360.

3 Properties of Geometrical Shapes NAME SHAPE PROPERTIES Square 1. It has four sides and four vertices. 2. All the sides are of equal length. 3. The measure of each angle is It has 2 diagonals. 5. Diagonals are of equal length. Rectangle 1. It has four sides and four vertices. 2. Opposite sides are equal in length. 3. The measure of each angle is It has two diagonals. 5. Diagonals are of equal length. Parallelogram 1. Opposite sides of are of equal length. 2. Opposite sides are parallel. 3. Opposite angles are of equal measure. 4. Adjacent angles are supplementary. 5. Diagonals bisect each other. 6. Sum of all the interior angles is 360.

4 Rhombus 1. All sides are of equal length. 2. Opposite sides are parallel. 3. Opposite angles are equal. 4. Diagonals are perpendicular bisectors of each other. 5. Sum of all the interior angles is 360. Trapezium 1. One pair of sides is parallel. 2. Adjacent angles made by non parallel side are supplementary. 3. Sum of all the interior angles is 360. In a parallelogram, opposite angles are equal. Conversely in a quadrilateral, if pair of opposite angles is equal, then the quadrilateral is a parallelogram. If in the quadrilateral PQRS, P = R and Q = S as shown in the above figure, then the quadrilateral is a parallelogram. The diagonals of a parallelogram bisect each other. Conversely, if the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Suppose ABCD is a quadrilateral. The diagonals of the quadrilateral intersect at O such that AO = OC and DO = OB

5 Therefore, ABCD is a parallelogram. The various views of this figure are as follows: Euler s Formula: For any polyhedron, F + V E = 2, where F is the number of faces, V is the number of vertices and E is the number of edges. Types of Regular polyhedra Tetrahedron

6 Hexahedron Octahedron Dodecahedron Icosahedron A prism is a polyhedron whose base and top are congruent polygons and whose lateral faces are parallelograms in shape.

7 A pyramid is a polyhedron whose base is a polygon (of any number of sides) and whose lateral faces are triangles with a common vertex. Area and Perimeter of various shapes Shape Area Perimeter Rectangle with adjacent sides a and b a b 2( a + b ) Square with side a a 2 4 a Circle with radius r πr 2 2 πr Triangle with base b and its corresponding height h Parallelogram with base b and its corresponding height h b h Sum of the three sides Sum of the four sides

8 Trapezium Sum of the four sides Area of quadrilateral ABCD = Area of ABC + Area of ACD Area of rhombus = Surface areas of cuboid: Lateral surface area of the cuboid = 2 h ( l + b ) Total surface area of the cuboid = 2 ( lb + bh + hl ) Note: Length of the diagonal of a cuboid =

9 Surface areas of cube: Lateral surface area of the cube = 4 a 2 Total surface area of the cube = 6 a 2 Note: Length of the diagonal of a cube = Surface areas of solid cylinder Curved surface area = 2π rh, where r and h are the radius and height Total surface area = 2π r ( r + h ), where r and h are the radius and height Volume of cube and cuboid Volume of cube = a 3, where a is the side of the cube Volume of cuboid = l b h, where l, b and h are respectively the length, breadth and height of the cuboid. Volume of the solid cylinder and hollow cylinder Volume of solid cylinder = π r 2 h, where r and h are the radius and height of the solid cylinder

10 Volume of the hollow cylinder = π ( R 2 r 2 ) h, where r, R and h are the inner radius, outer radius and height of hollow cylinder Relationship between common units of volume and capacity: 1 m l = 1 cm 3 1 l = 1000 cm 3 1 m 3 = cm 3 = 1000 l

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