Mensuration of 2D Shapes - Problems on Triangles - Case Studies

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Mensuration of 2D Shapes - Problems on Triangles - Case Studies MCQ & Objective Questions

Understanding the mensuration of 2D shapes, particularly triangles, is crucial for students preparing for various exams. This topic not only forms a significant part of the syllabus but also helps in enhancing problem-solving skills. Practicing MCQs and objective questions on this subject can significantly improve your exam preparation and boost your confidence in tackling important questions.

What You Will Practise Here

  • Key properties of triangles and their classifications
  • Formulas for calculating area, perimeter, and height of triangles
  • Understanding the concept of congruence and similarity in triangles
  • Application of the Pythagorean theorem in solving problems
  • Real-life case studies involving triangles in various contexts
  • Diagrams and visual aids to enhance conceptual clarity
  • Common problem-solving strategies for mensuration questions

Exam Relevance

The topic of mensuration of 2D shapes, especially problems on triangles, is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to apply formulas, analyze diagrams, and solve real-world problems. Common question patterns include direct calculations, conceptual applications, and multi-step problems that assess a student's understanding of the topic.

Common Mistakes Students Make

  • Confusing the formulas for area and perimeter
  • Overlooking the importance of units in calculations
  • Misinterpreting the properties of similar triangles
  • Neglecting to draw diagrams, which can lead to errors in understanding

FAQs

Question: What are the key formulas for calculating the area of a triangle?
Answer: The area of a triangle can be calculated using the formula: Area = 1/2 × base × height. Additionally, for equilateral triangles, the formula is Area = (√3/4) × side².

Question: How can I improve my speed in solving mensuration problems?
Answer: Regular practice of MCQs and objective questions will help you become familiar with different types of problems, improving both speed and accuracy.

Now is the time to enhance your understanding of mensuration! Dive into our practice MCQs and test your knowledge on important Mensuration of 2D Shapes - Problems on Triangles - Case Studies questions for exams. Your success starts with practice!

Q. A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5 cm, what is the area?
  • A. 12.5 cm²
  • B. 15 cm²
  • C. 10 cm²
  • D. 20 cm²
Q. A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. Is this triangle a right triangle?
  • A. Yes
  • B. No
  • C. Cannot be determined
  • D. Only if angles are known
Q. A triangle has two sides measuring 8 cm and 15 cm. If the angle between them is 60 degrees, what is the area of the triangle?
  • A. 60 cm²
  • B. 30 cm²
  • C. 40 cm²
  • D. 70 cm²
Q. If a triangle has a base of 15 cm and a height of 10 cm, what is the area?
  • A. 75 cm²
  • B. 150 cm²
  • C. 100 cm²
  • D. 50 cm²
Q. If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is its area?
  • A. 84 cm²
  • B. 168 cm²
  • C. 42 cm²
  • D. 56 cm²
Q. If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is the perimeter of the triangle?
  • A. 56 cm
  • B. 50 cm
  • C. 45 cm
  • D. 30 cm
Q. In an equilateral triangle with a side length of 6 cm, what is the area?
  • A. 9√3 cm²
  • B. 12 cm²
  • C. 18 cm²
  • D. 36 cm²
Q. What is the height of a triangle with an area of 36 cm² and a base of 12 cm?
  • A. 6 cm
  • B. 8 cm
  • C. 4 cm
  • D. 10 cm
Q. What is the length of the altitude from the vertex opposite the base of a triangle with a base of 10 cm and an area of 40 cm²?
  • A. 8 cm
  • B. 6 cm
  • C. 4 cm
  • D. 10 cm
Q. What is the semi-perimeter of a triangle with sides 10 cm, 14 cm, and 16 cm?
  • A. 20 cm
  • B. 25 cm
  • C. 30 cm
  • D. 22 cm
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