Introduction
Geometry is the branch of mathematics that studies shapes, sizes, angles and the positions of points, lines and figures. Mensuration is the applied part of geometry that measures length (perimeter), area and volume of two-dimensional (2D) and three-dimensional (3D) figures.
For Bangladeshi government job exams (BCS, Bank, and IT-officer posts) this topic is a guaranteed scorer. Almost every written and MCQ paper contains 2–5 questions on triangles, circles, quadrilaterals, angles, areas and volumes. The formulas are fixed, the logic is universal, and once you master a small set of relationships you can solve most questions in under a minute. This lesson builds every idea from first principles so that you not only memorise formulas but understand why they are true.
Learning objectives
By the end of this lesson you should be able to:
- Classify angles, lines, triangles and quadrilaterals and state their key properties.
- Apply the Pythagorean theorem and the properties of similar and congruent triangles.
- Use all standard perimeter and area formulas for 2D figures (triangle, rectangle, square, parallelogram, rhombus, trapezium, circle).
- Use surface-area and volume formulas for 3D solids (cube, cuboid, cylinder, cone, sphere, hemisphere).
- Work with circle theorems (central and inscribed angles, tangents, chords).
- Solve real exam problems on areas, perimeters, volumes and combined/shaded figures accurately and quickly.