18. Quadrilaterals and polygons
Free study material · concepts, shortcuts & solved questions
A quadrilateral’s interior angles sum to 360°. For a polygon with n sides, interior angle sum=(n−2)×180°. A regular polygon has equal sides and angles; each exterior angle is 360°/n and each interior angle is 180°−360°/n.
Method before formula Parallelogram has opposite sides and angles equal; rectangle has four right angles; rhombus has equal sides; square has both properties. A diagonal’s length may require Pythagoras. |
Formula and decision table
Shape | High-yield property |
Rectangle | Area=l×b; diagonal=√(l²+b²) |
Parallelogram | Area=base×height |
Regular hexagon | Each exterior angle=60° |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
Interior sum of a pentagon: | (5−2)×180=540°. | B. 540° |
Each exterior angle of a regular octagon: | 360/8=45°. | C. 45° |
Area of parallelogram is: | Perpendicular height is required. | A. base×height |
What an examiner is testing
The options around Quadrilaterals and polygons usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: Interior sum of a pentagon: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 540°, because (5−2)×180=540°.
Example 2: Each exterior angle of a regular octagon: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 45°, because 360/8=45°.
Example 3: Area of parallelogram is: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is base×height, because Perpendicular height is required.
Chapter practice
1. Interior sum of a pentagon:
(A) 360° (B) 540° (C) 720° (D) 900°
Answer: B. 540° | Explanation: (5−2)×180=540°.
2. Each exterior angle of a regular octagon:
(A) 30° (B) 40° (C) 45° (D) 60°
Answer: C. 45° | Explanation: 360/8=45°.
3. Area of parallelogram is:
(A) base×height (B) side² only (C) diagonal×2 (D) perimeter/2
Answer: A. base×height | Explanation: Perpendicular height is required.
SSC CGL speed and trap clinic
For Quadrilaterals and polygons, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Quadrilaterals and polygons? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Quadrilaterals and polygons question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |