Mensuration of 2D Shapes - Problems on Triangles

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

Understanding the mensuration of 2D shapes, especially triangles, is crucial for students preparing for school and competitive exams. This topic not only enhances your problem-solving skills but also helps you score better in MCQs and objective questions. By practicing a variety of problems, you can grasp essential concepts and tackle important questions with confidence during your exam preparation.

What You Will Practise Here

  • Calculating the area of different types of triangles: equilateral, isosceles, and scalene.
  • Understanding the properties of triangles and their significance in mensuration.
  • Applying the formula for the perimeter of triangles and solving related problems.
  • Using Heron's formula for finding the area of a triangle when side lengths are known.
  • Exploring the relationship between the height and base of triangles in area calculations.
  • Identifying and using key diagrams to visualize triangle problems effectively.
  • Solving real-life application problems involving triangles and their measurements.

Exam Relevance

The mensuration of 2D shapes, particularly problems on triangles, is a significant topic in various examinations such as CBSE, State Boards, NEET, and JEE. Questions often focus on calculating areas, perimeters, and applying properties of triangles. Common patterns include direct calculation problems, application-based scenarios, and conceptual questions that test your understanding of the subject.

Common Mistakes Students Make

  • Confusing the formulas for area and perimeter, leading to incorrect answers.
  • Overlooking the importance of units in calculations, which can affect the final result.
  • Misinterpreting the properties of different triangle types, causing errors in application.
  • Failing to visualize problems with diagrams, which can hinder understanding.

FAQs

Question: What is the formula for the area of a triangle?
Answer: The area of a triangle can be calculated using the formula: Area = 1/2 × base × height.

Question: How do I apply Heron's formula?
Answer: Heron's formula states that the area of a triangle can be calculated using the semi-perimeter and the lengths of its sides: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.

Now is the time to enhance your skills! Dive into our practice MCQs on Mensuration of 2D Shapes - Problems on Triangles and test your understanding. The more you practice, the better prepared you will be for your exams!

Q. A right triangle has legs of lengths 6 cm and 8 cm. What is the area of the triangle?
  • A. 24 cm²
  • B. 30 cm²
  • C. 48 cm²
  • D. 36 cm²
Q. A triangle has an area of 48 cm² and a base of 8 cm. What is the height?
  • A. 12 cm
  • B. 6 cm
  • C. 8 cm
  • D. 10 cm
Q. A triangle has sides of lengths 9 cm, 12 cm, and 15 cm. Is it a right triangle?
  • A. Yes
  • B. No
  • C. Cannot be determined
  • D. Only if angles are known
Q. A triangle has vertices at (0, 0), (4, 0), and (0, 3). What is its area?
  • A. 6 cm²
  • B. 12 cm²
  • C. 8 cm²
  • D. 10 cm²
Q. If a triangle has an area of 36 cm² and a base of 9 cm, what is its height?
  • A. 8 cm
  • B. 6 cm
  • C. 4 cm
  • D. 10 cm
Q. If the lengths of the sides of a triangle are 5 cm, 12 cm, and 13 cm, what type of triangle is it?
  • A. Acute
  • B. Obtuse
  • C. Right
  • D. Equilateral
Q. If the lengths of two sides of a triangle are 5 cm and 12 cm, and the included angle is 90 degrees, what is the area?
  • A. 30 cm²
  • B. 60 cm²
  • C. 24 cm²
  • D. 20 cm²
Q. If the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is its area?
  • A. 84 cm²
  • B. 96 cm²
  • C. 120 cm²
  • D. 72 cm²
Q. In a right triangle, if one leg is 6 cm and the other leg is 8 cm, what is the area?
  • A. 24 cm²
  • B. 30 cm²
  • C. 48 cm²
  • D. 36 cm²
Q. What is the area of an isosceles triangle with a base of 10 cm and equal sides of 13 cm?
  • A. 60 cm²
  • B. 65 cm²
  • C. 70 cm²
  • D. 75 cm²
Q. What is the height of a triangle with an area of 60 cm² and a base of 12 cm?
  • A. 10 cm
  • B. 5 cm
  • C. 8 cm
  • D. 6 cm
Q. What is the length of the altitude to the base of a triangle with an area of 50 cm² and a base of 10 cm?
  • A. 10 cm
  • B. 5 cm
  • C. 15 cm
  • D. 20 cm
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