SSC Foundation Batch 2024 | SSC Maths | Mensuration #1 | SSC Exam | Maths By Ravinder Sir

SSC Wallah・2 minutes read

Mensuration is a key topic in various competitive exams with multiple questions dedicated to it, including important formulas for triangles and circles. Patience and revision are essential for effective problem-solving, as understanding geometric shapes and properties is crucial for accurate calculations.

Insights

  • Mensuration is a significant topic in competitive exams, with varying numbers of questions from it depending on the exam, such as 6 in CPO, 2-3 in CGL, CHSL, and MTS, 8-10 in CDS, and 1-2 in state-level exams.
  • Equilateral triangles are vital in mensuration, with key formulas for perimeter and height, while the radius ratio of circles inside and outside these triangles is fixed at 1:2, and perpendiculars drawn on their sides are always divisible by two.

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Recent questions

  • What is the importance of mensuration in competitive exams?

    Mensuration is a crucial concept in competitive exams, with a significant number of questions dedicated to this topic. In exams like CPO, CGL, CHSL, MTS, CDS, Delhi Police, and state-level exams, questions related to mensuration are common. Understanding mensuration is essential for scoring well in these exams, as questions can range from equilateral triangles to circles inside different shapes. Being well-versed in mensuration formulas and concepts can greatly enhance your performance in competitive exams.

  • What are the key properties of equilateral triangles in mensuration?

    Equilateral triangles play a significant role in mensuration, with key formulas like perimeter being 3a and height being √3/2 of a. The radius of circles inside and outside equilateral triangles is crucial, with the ratio of the radii being fixed at 1:2. Perpendiculars drawn on all sides of an equilateral triangle are always divisible by two. Understanding these properties and formulas related to equilateral triangles is essential for solving mensuration questions accurately and efficiently.

  • How are isosceles triangles calculated in mensuration?

    Isosceles triangles have equal sides, with formulas for area involving base and height calculations. By understanding the properties of isosceles triangles, such as equal sides and specific area formulas, you can effectively solve mensuration questions related to this type of triangle. Being familiar with the calculations and properties of isosceles triangles is crucial for success in competitive exams.

  • What are the properties of right-angled triangles in mensuration?

    Right-angled triangles have a 90-degree angle, with specific formulas for finding the radius of circles inside and outside them. Understanding the properties of right-angled triangles, such as the relationship between sides and angles, is essential for solving mensuration questions accurately. By knowing the formulas and properties related to right-angled triangles, you can approach these types of questions with confidence in competitive exams.

  • How can knowledge of geometric shapes aid in mensuration problem-solving?

    Understanding geometric shapes and their properties is crucial for accurate calculations in mensuration. Whether it's equilateral triangles, isosceles triangles, right-angled triangles, squares, rhombuses, or quadrilaterals, knowing the properties and formulas associated with these shapes is essential for solving mensuration questions effectively. By familiarizing yourself with geometric shapes and their characteristics, you can approach mensuration problems with confidence and improve your performance in competitive exams.

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Summary

00:00

Importance of Mensuration in Competitive Exams

  • Mensuration is a crucial concept in competitive exams, with at least 6 questions out of 50 being from this topic in exams like CPO.
  • In CGL, 2-3 questions are from mensuration, while in CHSL and MTS, 2-3 questions are also included.
  • The importance of mensuration is evident in various exams, with 8-10 questions in CDS, 2 questions in Delhi Police, and 1-2 questions in state-level exams.
  • Equilateral triangles play a significant role in mensuration, with key formulas like perimeter being 3a and height being √3/2 of a.
  • The radius of circles inside and outside equilateral triangles is crucial, with the ratio of the radii being fixed at 1:2.
  • Perpendiculars drawn on all sides of an equilateral triangle are always divisible by two.
  • Isosceles triangles have equal sides, with formulas for area involving base and height calculations.
  • Scalene triangles are calculated using Hero's formula, with the area being under the root of s, s-a, s-b, and s-c.
  • Right-angled triangles have a 90-degree angle, with formulas for finding the radius of circles inside and outside them.
  • General formulas for finding the radius of circles inside and outside any triangle involve the area divided by the semi-perimeter and the product of all sides divided by 4 times the area, respectively.

16:44

Geometric Shapes and Their Properties

  • Isosceles triangle with equal sides and area 4a; radius of circles inside and outside can be found by producing sides.
  • Square with all sides equal to A; perimeter 4a, area A square, diagonal root 2a.
  • Transformation of square into rhombus; perimeter 4a, area diagonal AC into diagonal DC.
  • Area of any quadrilateral can be found by base times height or diagonals intersecting at 90 degrees.
  • Diagonals of rhombus intersect at 90 degrees; angle bisectors are equal.
  • Relation between square and rhombus due to changing square angles.
  • Radius inside square is half of side; outside square, radius equals diagonal.
  • Circle inside square and outside square have radius ratio of 1 to root 2.
  • Equilateral triangle's circumradius is a in root 3; perpendiculars relation with sides is 2 times p1 p2 p3.
  • Proof of equilateral triangle perpendiculars relation; area divided into three parts.

31:59

Mastering Geometry: Key Tips for Success

  • Multiplying by Rati at the top and bottom simplifies question-solving process
  • Patience is key to understanding and solving questions effectively
  • Revising questions multiple times aids in comprehension and accuracy
  • Ratio of area of inscribed circle to circumference of N Square causes confusion
  • Answering questions in comment section helps AI system track and rank responses
  • Misunderstanding question details leads to incorrect answers
  • Understanding rhombus properties aids in calculating diagonal lengths
  • Knowledge of triplets assists in solving geometric questions efficiently
  • Understanding geometric shapes and their properties is crucial for accurate calculations
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