Quantitative Aptitude on Plane Shapes and Scale Drawing

Quantitative Aptitude on Plane Shapes and Scale Drawing

i. Definition

Quantitative aptitude on plane shapes and scale drawing refers to the ability to reason and solve problems related to two-dimensional shapes, such as points, lines, angles, triangles, quadrilaterals, polygons, and circles, as well as the skill to interpret and create scale drawings. It involves understanding the properties, relationships, and measurements of these shapes, and applying mathematical concepts to solve problems.

ii. Reasons for Studying Quantitative Aptitude

Studying quantitative aptitude on plane shapes and scale drawing is essential for several reasons:

1. Development of Problem-Solving Skills: It helps students develop critical thinking, logical reasoning, and analytical skills, which are valuable in various aspects of life.
2. Improvement of Spatial Awareness: Understanding plane shapes and scale drawing enhances spatial awareness, enabling students to visualize and interpret geometric shapes and relationships.
3. Enhancement of Mathematical Concepts: It reinforces mathematical concepts, such as geometry, measurement, and proportions, which are crucial in various fields, including science, technology, engineering, and mathematics (STEM).
4. Real-World Applications: Quantitative aptitude on plane shapes and scale drawing has numerous real-world applications, such as architecture, engineering, design, and art.
5. Preparation for Further Education: It provides a solid foundation for advanced mathematical studies and prepares students for more complex geometric and spatial reasoning concepts.

iii. Solving Problems on Quantitative Reasoning

Here are some examples of problems on quantitative reasoning on plane shapes and scale drawing:

Problem 1: In a scale drawing, a room is represented by a rectangle with a length of 6 cm and a width of 4 cm. If the scale is 1:50, what are the actual dimensions of the room?

Solution: To find the actual dimensions, multiply the scale drawing measurements by the scale factor (50). Length: 6 cm x 50 = 300 cm = 3 m Width: 4 cm x 50 = 200 cm = 2 m

Problem 2: A triangle has an angle of 60° and a side opposite to the angle of 8 cm. What is the length of the side adjacent to the angle?

Solution: Using trigonometry, we can find the length of the adjacent side: tan(60°) = opposite side / adjacent side adjacent side = opposite side / tan(60°) = 8 cm / √3 = 4.62 cm (approximately)

Problem 3: A scale drawing of a building has a height of 10 cm and a base of 5 cm. If the scale is 1:100, what is the actual height and base of the building?

Solution: To find the actual dimensions, multiply the scale drawing measurements by the scale factor (100). Height: 10 cm x 100 = 1000 cm = 10 m Base: 5 cm x 100 = 500 cm = 5 m

These problems demonstrate the application of quantitative aptitude on plane shapes and scale drawing, requiring students to reason and solve problems using mathematical concepts and spatial awareness.