Mensuration

After completion of this chapter, students will be able to:

  • find the area of triangles (right angled, equilateral, isosceles and scalene).
  • solve the practical problems related to the area of triangles.
  • find the surface area and volume of a triangular prism.
  • find the surface area and volume of cylinder, sphere, cone and pyramid.
  • find the surface area and volume of combined solids made by cylinder, cone, sphere etc.

Notes

Area of Triangle

The area of a triangle is always half the product of the height and base.A triangle is a polygon with three edges and three vertices.A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse, the longest side of the triangle.

Triangular prism

A triangular prism is a prism composed of two triangular bases and three rectangular sides. A prism with the triangle as the base is called triangular prism. In case of triangular prism, two congruent and parallel triangles

Cylinder

A hollow cylinder can be formed by rolling and joining two breadth of the rectangular sheet of paper. A Cylinder is a prism consisting of two parallel congruent circular bases.

Sphere and Hemisphere

The sphere is a solid object whose each point in the outer surface is equidistance from the fixed point inside it. Such a fixed point is called the centre of the sphere. The constant distance is called the radius of the sphere. Solid object such as globe, volleyball, toy ball, table tennis ball, marble etc are the example of sphere.

Cone

A cone is a solid object whose base is a circle and another part is a smooth curved surface that symmetrically ends at a point in space. The point is called the vertex of the cone. The line segments that joins the centre of the base and the vertex is called the height of the cone. Line segments that joins the vertex to the point of the circumference of the base circle is called the generator. The length of the generator is called the slant height of the cone. If the axis is perpendicular to the base of circ

Pyramid

The pyramid is solid with polygonal base and triangular faces with common vertex. A line through the vertex to the centre of the base is called the height of the pyramid. Height is perpendicular to the base is called a right pyramid otherwise pyramid is oblique pyramid. Height is perpendicular to the base is called right pyramid otherwise pyramid is oblique pyramid. A pyramid is regular if it's all lateral faces are congruent isosceles triangle.Surface area of the pyramid is the total surface area of its al