Geometry and mensuration basics
Connect each measurement formula to the shape and dimension it describes.
Angles#
Angles on a straight line total 180°, angles around a point total 360°, and the interior angles of a triangle total 180°. These relationships help find missing values without measuring a drawing.
Perimeter and area#
Perimeter is the total boundary length. A rectangle with length l and width w has perimeter 2(l + w) and area lw.
A triangle has area one half × base × perpendicular height. The height must meet the chosen base at a right angle.
A circle with radius r has circumference 2πr and area πr². The diameter is 2r.
Volume#
A rectangular prism has volume length × width × height. A cylinder has volume πr²h. Volume measures three-dimensional space, so its units are cubic.
Composite shapes#
Break a complicated figure into familiar shapes, calculate each part, and add or subtract as the diagram requires. Mark shared edges so they are not counted twice in a perimeter.
Unit discipline#
Convert lengths before using a formula. One metre equals 100 centimetres, but one square metre equals 10,000 square centimetres because both dimensions scale.
Common mistakes#
Do not confuse radius and diameter, sloping side and perpendicular height, or area and perimeter. A formula should match the requested dimension.
Final check#
Label known values, write units at every stage, estimate the result, and ask whether the magnitude fits the drawing.
Key points
- Perimeter measures boundary length, area measures surface, and volume measures space.
- Triangle angles total 180 degrees and angles around a point total 360 degrees.
- Area uses square units and volume uses cubic units.
- Draw and label the figure before selecting a formula.